![\"$0-9$\"](\"\/\/latex.artofproblemsolving.com\/5\/3\/4\/53458ebc12bfd4c66c5cad57012a1200803297e1.png\")
exactly once.<\/li>\n![\"$+$\"](\"\/\/latex.artofproblemsolving.com\/7\/7\/c\/77cf26be132ef93923e082ee4153b2cb0ef44a50.png\")
,<\/span> ![\"$-$\"](\"\/\/latex.artofproblemsolving.com\/a\/d\/d\/add22d9bda21e86390bc74fa4dde17730a442da7.png\")
,<\/span> ![\"$\\div$\"](\"\/\/latex.artofproblemsolving.com\/1\/c\/8\/1c81486a525ba08192aab8546dbe9a32bdbe0c07.png\")
,<\/span> ![\"$\\times$\"](\"\/\/latex.artofproblemsolving.com\/b\/a\/c\/bac4dbe1c696d11e8dc43dd7f613199b2120daa1.png\")
,<\/span> and parentheses<\/li>\ndenote concatenation using ![\"$||$\"](\"\/\/latex.artofproblemsolving.com\/b\/9\/5\/b95f37a176047e59b4af0f347d1e9d07e3a61fa9.png\")
,<\/span> so ![\"$4](\"\/\/latex.artofproblemsolving.com\/a\/b\/d\/abdac5abb5c13aab8217b66ad84d699e53acd54e.png\")
<\/div><\/li>\n- and you are allowed to use logarithms, although the base must be written except when using the natural log<\/li>\n<\/ul>\n
\nThen, try doing it if you are allowed to use tetration<\/span>
,<\/span> so <\/div><\/li>\n\nThen, try doing it if you are allowed to use tetration<\/span>
for tetration, denote tetration as ![\"$b^{b^{b^{\\cdot^{\\cdot^{\\cdot^](\"\/\/latex.artofproblemsolving.com\/3\/b\/7\/3b797951a62e0cbaea42fd4545a5f396565b3907.png\")
,<\/span> where there are ![\"$a$\"](\"\/\/latex.artofproblemsolving.com\/c\/7\/d\/c7d457e388298246adb06c587bccd419ea67f7e8.png\")
![\"$b$\"](\"\/\/latex.artofproblemsolving.com\/8\/1\/3\/8136a7ef6a03334a7246df9097e5bcc31ba33fd2.png\")
'<\/span>s in the exponentiation tower. for example, ![\"$^37=7^{7^7}$\"](\"\/\/latex.artofproblemsolving.com\/3\/7\/9\/37970bb948c4ca0aadd1d4f1e9443d646b5d9dfb.png\")
<\/div>","post_canonical":"Make the largest number you can under the following rules:\n\n[list]\n[*] You must use each of the integers $0-9$ exactly once.\n[*] You are allowed to use any of the four operations $+$, $-$, $\\div$, $\\times$, and parentheses\n[*]You are allowed to use exponentiation\n[*] You are allowed to use [hide=concatenation] denote concatenation using $||$, so $4 || 7=47$[\/hide]\n[*] and you are allowed to use logarithms, although the base must be written except when using the natural log\n[\/list]\n\nThen, try doing it if you are allowed to use [hide=tetration]for tetration, denote tetration as $b^{b^{b^{\\cdot^{\\cdot^{\\cdot^ b}}}}}=^ab$, where there are $a$ $b$'s in the exponentiation tower. for example, $^37=7^{7^7}$[\/hide]","username":"eagles2018","reported":false,"is_thanked":false,"is_nothanked":false,"attachment":false,"thanks_received":7,"nothanks_received":0,"thankers":"violin21, tennisrules, HWenslawski, ImSh95, asimov, son7, TsunamiStorm08","deleted":false,"post_number":1,"post_time":1652322082,"num_edits":0,"post_format":"bbcode","last_edit_time":0,"last_editor_username":"","last_edit_reason":"","admin":false,"avatar":"\/\/avatar.artofproblemsolving.com\/avatar_541699.png?t=1594928893","num_posts":2292,"editable":false,"deletable":false,"show_from_start":true,"show_from_end":false}],"topic_id":2843284,"comment_count":52,"num_deleted":3,"topic_title":"Challenge: The biggest number","target_url":"","target_text":"","topic_type":"forum","state":"none","first_post_id":25190306,"first_poster_id":541699,"first_post_time":1652322082,"first_poster_name":"eagles2018","last_post_time":1653070737,"first_poster_avatar":"\/\/avatar.artofproblemsolving.com\/avatar_541699.png?t=1594928893","last_poster_avatar":"\/\/avatar.artofproblemsolving.com\/avatar_402075.jpg?t=1631296469","last_post_id":25250384,"last_poster_id":402075,"last_poster_name":"fruitmonster97","last_update_time":1653070737,"category_id":3,"is_public":true,"roles":{"38516":"mod","53544":"mod","242520":"mod"},"tags":[{"tag_id":31454,"tag_text":"maximum","is_visible":true},{"tag_id":177,"tag_text":"number theory","is_visible":true},{"tag_id":30508,"tag_text":"challenge","is_visible":true}],"can_have_source":false,"locked":false,"forum_locked":0,"announce_type":"none","announce_through":"","announce_factor":0,"preview":"Make the largest number you can under the following rules:
\n
\n[list]
\n[*] You must use each of the integers exactly once.
\n[*] You are allowed to use any of the four operations,<\/span> ,<\/span> ,<\/span> ,<\/span> and parentheses
\n[*]You are allowed to use exponentiation
\n[*] You are allowed to use concatenation<\/span>
,<\/span> where there are '<\/span>s in the exponentiation tower. for example, <\/div>","post_canonical":"Make the largest number you can under the following rules:\n\n[list]\n[*] You must use each of the integers $0-9$ exactly once.\n[*] You are allowed to use any of the four operations $+$, $-$, $\\div$, $\\times$, and parentheses\n[*]You are allowed to use exponentiation\n[*] You are allowed to use [hide=concatenation] denote concatenation using $||$, so $4 || 7=47$[\/hide]\n[*] and you are allowed to use logarithms, although the base must be written except when using the natural log\n[\/list]\n\nThen, try doing it if you are allowed to use [hide=tetration]for tetration, denote tetration as $b^{b^{b^{\\cdot^{\\cdot^{\\cdot^ b}}}}}=^ab$, where there are $a$ $b$'s in the exponentiation tower. for example, $^37=7^{7^7}$[\/hide]","username":"eagles2018","reported":false,"is_thanked":false,"is_nothanked":false,"attachment":false,"thanks_received":7,"nothanks_received":0,"thankers":"violin21, tennisrules, HWenslawski, ImSh95, asimov, son7, TsunamiStorm08","deleted":false,"post_number":1,"post_time":1652322082,"num_edits":0,"post_format":"bbcode","last_edit_time":0,"last_editor_username":"","last_edit_reason":"","admin":false,"avatar":"\/\/avatar.artofproblemsolving.com\/avatar_541699.png?t=1594928893","num_posts":2292,"editable":false,"deletable":false,"show_from_start":true,"show_from_end":false}],"topic_id":2843284,"comment_count":52,"num_deleted":3,"topic_title":"Challenge: The biggest number","target_url":"","target_text":"","topic_type":"forum","state":"none","first_post_id":25190306,"first_poster_id":541699,"first_post_time":1652322082,"first_poster_name":"eagles2018","last_post_time":1653070737,"first_poster_avatar":"\/\/avatar.artofproblemsolving.com\/avatar_541699.png?t=1594928893","last_poster_avatar":"\/\/avatar.artofproblemsolving.com\/avatar_402075.jpg?t=1631296469","last_post_id":25250384,"last_poster_id":402075,"last_poster_name":"fruitmonster97","last_update_time":1653070737,"category_id":3,"is_public":true,"roles":{"38516":"mod","53544":"mod","242520":"mod"},"tags":[{"tag_id":31454,"tag_text":"maximum","is_visible":true},{"tag_id":177,"tag_text":"number theory","is_visible":true},{"tag_id":30508,"tag_text":"challenge","is_visible":true}],"can_have_source":false,"locked":false,"forum_locked":0,"announce_type":"none","announce_through":"","announce_factor":0,"preview":"Make the largest number you can under the following rules:\n
\n[list]
\n[*] You must use each of the integers
exactly once.\n[*] You are allowed to use any of the four operations
,<\/span> ,<\/span> ,<\/span> ,<\/span> and parentheses\n[*]You are allowed to use exponentiation
\n[*] You are allowed to use concatenation<\/span>
denote concatenation using ,<\/span> so <\/div>
\n[*] and you are allowed to use logarithms, although the base must be written except when using the natural log
\n[\/list]
\n
\nThen, try doing it if you are allowed to use tetration<\/span>
,<\/span> so <\/div>\n[*] and you are allowed to use logarithms, although the base must be written except when using the natural log
\n[\/list]
\n
\nThen, try doing it if you are allowed to use tetration<\/span>
for tetration, denote tetration as ,<\/span> where there are '<\/span>s in the exponentiation tower. for example, <\/div>","category_name":"Middle School Math","category_main_color":"#f90","category_secondary_color":"#fff5d4","num_reports":0,"poll_id":0,"source":"","category_num_users":13,"category_num_topics":46945,"category_num_posts":659603,"num_views":2146,"cat_can_target":0,"has_thanks":true,"has_nothanks":false,"is_bookmarked":false,"in_feed":false,"is_watched":false},"2847200":{"num_posts":77,"posts_data":[{"post_id":25233412,"topic_id":2847200,"poster_id":623822,"post_rendered":"Choose the option that is closest","post_canonical":"Choose the option that is closest","username":"URcurious2","reported":false,"is_thanked":false,"is_nothanked":false,"attachment":false,"thanks_received":2,"nothanks_received":0,"thankers":"ImSh95, At777","deleted":false,"post_number":1,"post_time":1652854411,"num_edits":0,"post_format":"bbcode","last_edit_time":0,"last_editor_username":"","last_edit_reason":"","admin":false,"avatar":"\/\/avatar.artofproblemsolving.com\/avatar_623822.png?t=1610748309","num_posts":117,"editable":false,"deletable":false,"show_from_start":true,"show_from_end":false}],"topic_id":2847200,"comment_count":77,"num_deleted":2,"topic_title":"AIME to MathCounts ratio","target_url":"","target_text":"","topic_type":"forum","state":"none","first_post_id":25233412,"first_poster_id":623822,"first_post_time":1652854411,"first_poster_name":"URcurious2","last_post_time":1653070161,"first_poster_avatar":"\/\/avatar.artofproblemsolving.com\/avatar_623822.png?t=1610748309","last_poster_avatar":"\/\/avatar.artofproblemsolving.com\/avatar_775860.png?t=1647808405","last_post_id":25250340,"last_poster_id":775860,"last_poster_name":"Inaaya","last_update_time":1653070161,"category_id":3,"is_public":true,"roles":{"38516":"mod","53544":"mod","242520":"mod"},"tags":[{"tag_id":3,"tag_text":"AMC","is_visible":true},{"tag_id":183,"tag_text":"AIME","is_visible":true},{"tag_id":259,"tag_text":"ratio","is_visible":true},{"tag_id":29911,"tag_text":"poll","is_visible":true}],"can_have_source":false,"locked":false,"forum_locked":0,"announce_type":"none","announce_through":"","announce_factor":0,"preview":"Choose the option that is closest","category_name":"Middle School Math","category_main_color":"#f90","category_secondary_color":"#fff5d4","num_reports":0,"poll_id":47117,"source":"","category_num_users":13,"category_num_topics":46945,"category_num_posts":659603,"num_views":1850,"cat_can_target":0,"has_thanks":true,"has_nothanks":false,"is_bookmarked":false,"in_feed":false,"is_watched":false}};AoPS.preload_topics[4]={"2844078":{"num_posts":4,"posts_data":[{"post_id":25198764,"topic_id":2844078,"poster_id":244795,"post_rendered":"How many the number of arrangements of the letters AAAABBBC in which either the A's appear together in a block of four letters or the B's appear together in a block of three letters?
\n
\nCould you tell the answer and the explanation?","post_canonical":"How many the number of arrangements of the letters AAAABBBC in which either the A's appear together in a block of four letters or the B's appear together in a block of three letters?\n\nCould you tell the answer and the explanation?","username":"bsming","reported":false,"is_thanked":false,"is_nothanked":false,"attachment":false,"thanks_received":1,"nothanks_received":0,"thankers":"ImSh95","deleted":false,"post_number":1,"post_time":1652436811,"num_edits":0,"post_format":"bbcode","last_edit_time":0,"last_editor_username":"","last_edit_reason":"","admin":false,"avatar":"\/\/avatar.artofproblemsolving.com\/avatar_244795.png","num_posts":35,"editable":false,"deletable":false,"show_from_start":true,"show_from_end":false}],"topic_id":2844078,"comment_count":4,"num_deleted":0,"topic_title":"arrangements of the letters AAAABBBC","target_url":"","target_text":"","topic_type":"forum","state":"none","first_post_id":25198764,"first_poster_id":244795,"first_post_time":1652436811,"first_poster_name":"bsming","last_post_time":1653069633,"first_poster_avatar":"\/\/avatar.artofproblemsolving.com\/avatar_244795.png","last_poster_avatar":"\/\/avatar.artofproblemsolving.com\/avatar_1313.png","last_post_id":25250283,"last_poster_id":1313,"last_poster_name":"gauss202","last_update_time":1653069633,"category_id":4,"is_public":true,"roles":{"38516":"mod","242520":"mod","53544":"mod"},"tags":[{"tag_id":139072,"tag_text":"MATHCOUNTS prep","is_visible":true}],"can_have_source":false,"locked":false,"forum_locked":0,"announce_type":"none","announce_through":"","announce_factor":0,"preview":"How many the number of arrangements of the letters AAAABBBC in which either the A's appear together in a block of four letters or the B's appear together in a block of three letters?
\n
\nCould you tell the answer and the explanation?","category_name":"High School Math","category_main_color":"#e75400","category_secondary_color":"#ffe7cc","num_reports":0,"poll_id":0,"source":"","category_num_users":8,"category_num_topics":103885,"category_num_posts":565535,"num_views":235,"cat_can_target":0,"has_thanks":true,"has_nothanks":false,"is_bookmarked":false,"in_feed":false,"is_watched":false},"2848183":{"num_posts":2,"posts_data":[{"post_id":25243640,"topic_id":2848183,"poster_id":167643,"post_rendered":"In triangle![\"$ABC$\"](\"\/\/latex.artofproblemsolving.com\/e\/2\/a\/e2a559986ed5a0ffc5654bd367c29dfc92913c36.png\")
with angles ![\"$\\angle](\"\/\/latex.artofproblemsolving.com\/6\/0\/6\/606e48e5ea682394ddf3cae870f5fc5bdcd98299.png\")
and ![\"$\\angle](\"\/\/latex.artofproblemsolving.com\/b\/d\/d\/bddbb513df793a91f335bfb77ba43d14bcd55a4b.png\")
on segment ![\"$BC$\"](\"\/\/latex.artofproblemsolving.com\/6\/c\/5\/6c52a41dcbd739f1d026c5d4f181438b75b76976.png\")
,<\/span> a point ![\"$D$\"](\"\/\/latex.artofproblemsolving.com\/9\/f\/f\/9ffb448918db29f2a72f8f87f421b3b3cad18f95.png\")
is chosen such that ![\"$2](\"\/\/latex.artofproblemsolving.com\/0\/e\/0\/0e0643fdf9f0062421fc69967aa84bfbfd63bab1.png\")
and ![\"$M$\"](\"\/\/latex.artofproblemsolving.com\/5\/d\/1\/5d1e4485dc90c450e8c76826516c1b2ccb8fce16.png\")
is the midpoint of segment ![\"$AC$\"](\"\/\/latex.artofproblemsolving.com\/a\/1\/7\/a179ff2638e4799cadd820db205c2beff6299ce9.png\")
.<\/span> Find ![\"$\\angle](\"\/\/latex.artofproblemsolving.com\/d\/e\/7\/de73b9742eac7d4adfff2b13361e3bceaac9c8f9.png\")
.<\/span>","post_canonical":"In triangle $ABC$ with angles $\\angle ACB = 40^o$ and $\\angle BAC = 60^o$ on segment $BC$, a point $D$ is chosen such that $2 \\cdot CD = AB$ and $M$ is the midpoint of segment $AC$. Find $\\angle CMD$.","username":"parmenides51","reported":false,"is_thanked":false,"is_nothanked":false,"attachment":false,"thanks_received":0,"nothanks_received":0,"thankers":null,"deleted":false,"post_number":1,"post_time":1652986328,"num_edits":0,"post_format":"bbcode","last_edit_time":0,"last_editor_username":"","last_edit_reason":"","admin":false,"avatar":"\/\/avatar.artofproblemsolving.com\/avatar_167643.png?t=1472410314","num_posts":18897,"editable":false,"deletable":false,"show_from_start":true,"show_from_end":false}],"topic_id":2848183,"comment_count":2,"num_deleted":0,"topic_title":"<CMD=? 100-60-40 triangle, 2CD=AB 2022 Russian Young Mathematician 6-7.8","target_url":"","target_text":"","topic_type":"forum","state":"none","first_post_id":25243640,"first_poster_id":167643,"first_post_time":1652986328,"first_poster_name":"parmenides51","last_post_time":1653069099,"first_poster_avatar":"\/\/avatar.artofproblemsolving.com\/avatar_167643.png?t=1472410314","last_poster_avatar":"\/\/avatar.artofproblemsolving.com\/avatar_36948.jpg","last_post_id":25250239,"last_poster_id":36948,"last_poster_name":"sunken rock","last_update_time":1653069099,"category_id":4,"is_public":true,"roles":{"38516":"mod","242520":"mod","53544":"mod"},"tags":[{"tag_id":48,"tag_text":"geometry","is_visible":true},{"tag_id":45165,"tag_text":"angles","is_visible":true},{"tag_id":1629561,"tag_text":"Young Mathematician","is_visible":true}],"can_have_source":false,"locked":false,"forum_locked":0,"announce_type":"none","announce_through":"","announce_factor":0,"preview":"In triangle with angles and on segment ,<\/span> a point is chosen such that and is the midpoint of segment .<\/span> Find .<\/span>","category_name":"High School Math","category_main_color":"#e75400","category_secondary_color":"#ffe7cc","num_reports":0,"poll_id":0,"source":"","category_num_users":8,"category_num_topics":103885,"category_num_posts":565535,"num_views":59,"cat_can_target":0,"has_thanks":true,"has_nothanks":false,"is_bookmarked":false,"in_feed":false,"is_watched":false},"2835578":{"num_posts":2,"posts_data":[{"post_id":25102300,"topic_id":2835578,"poster_id":167643,"post_rendered":"VI.<\/b> Rounds 1-4<\/u>
\n
\n
\n1.2<\/b>![\"$9$\"](\"\/\/latex.artofproblemsolving.com\/b\/f\/2\/bf2c9074b396e3af0dea52d792660eea1c77f10f.png\")
numbers are written out, the lengths of the angle bisectors, altitudes and medians of a certain triangle. It is known that among them there are no more than ![\"$4$\"](\"\/\/latex.artofproblemsolving.com\/c\/7\/c\/c7cab1a05e1e0c1d51a6a219d96577a16b7abf9d.png\")
different ones. Prove that this triangle is isosceles.
\n
\n
\n1.3<\/b> Is it possible to cut a cube into 6 equal triangular pyramids?
\n
\n
\n1.6 <\/b> All points of the strip of width 0.001 are colored in two colors. Prove that there are two points of the same color at a distance of 1.
\n
\n
\n1.7<\/b> On sides,<\/span> ![\"$CA$\"](\"\/\/latex.artofproblemsolving.com\/e\/6\/5\/e657259c0995d2c36d46744bb4aa81471e6575ec.png\")
and ![\"$AB$\"](\"\/\/latex.artofproblemsolving.com\/5\/7\/e\/57ee5125358c0606c9b588580ddfa66f83e607b7.png\")
of triangle ABC, points ![\"$A_1$\"](\"\/\/latex.artofproblemsolving.com\/3\/6\/c\/36c7f3f828cf12ab9cafeffad282468a95219600.png\")
,<\/span> ![\"$B_1$\"](\"\/\/latex.artofproblemsolving.com\/2\/4\/3\/243af6fad28c15abb3e11996374ba60e745bf543.png\")
and ![\"$C_1$\"](\"\/\/latex.artofproblemsolving.com\/7\/0\/b\/70b97eb4ad6e4e7a5a97e2547d9ed6e965960d0c.png\")
are taken respectively so that ![\"$$AC_1:C_1B](\"\/\/latex.artofproblemsolving.com\/3\/d\/9\/3d986133b5881edc28896966ce4e393c1c4907f1.png\")
Prove that if triangle ![\"$A_1B_1C_1$\"](\"\/\/latex.artofproblemsolving.com\/9\/b\/1\/9b1815ca31a0a4b18b725b690862a84de67aed84.png\")
is equilateral, then triangle is also equilateral.
\n
\n
\n2.5<\/b> On sides![\"$CD$\"](\"\/\/latex.artofproblemsolving.com\/0\/9\/4\/0948661e822f2a953c43a57ac9e40b2734476de4.png\")
and ![\"$DA$\"](\"\/\/latex.artofproblemsolving.com\/0\/b\/3\/0b31cd391bebc36897a8c10ea78e5d584980b049.png\")
of parallelogram ![\"$ABCD$\"](\"\/\/latex.artofproblemsolving.com\/f\/9\/e\/f9efaf9474c5658c4089523e2aff4e11488f8603.png\")
,<\/span> points ![\"$E$\"](\"\/\/latex.artofproblemsolving.com\/f\/a\/2\/fa2fa899f0afb05d6837885523503a2d4df434f9.png\")
and ![\"$F$\"](\"\/\/latex.artofproblemsolving.com\/a\/0\/5\/a055f405829e64a3b70253ab67cb45ed6ed5bb29.png\")
are taken, respectively. Let ![\"$K$\"](\"\/\/latex.artofproblemsolving.com\/d\/f\/b\/dfb064112b6c94470339f6571f69d07afc1c024c.png\")
be the intersection point of segments ![\"$AE$\"](\"\/\/latex.artofproblemsolving.com\/9\/a\/6\/9a65c05bd85d2609bea5db2b109ed5f556463511.png\")
and ![\"$CF$\"](\"\/\/latex.artofproblemsolving.com\/0\/7\/d\/07d29465728e92952374a857beaee91665d8dbd9.png\")
.<\/span> Prove that if the areas of triangles ![\"$AKF$\"](\"\/\/latex.artofproblemsolving.com\/c\/e\/6\/ce6bc740cb6cb591e4787222c09218c7130355f1.png\")
and ![\"$CKE$\"](\"\/\/latex.artofproblemsolving.com\/c\/d\/b\/cdbde756c78aa0f706791826b72f87f17a154349.png\")
are equal, then the point lies on the diagonal ![\"$BD$\"](\"\/\/latex.artofproblemsolving.com\/8\/9\/f\/89fff82bb65d0215e49c8c91cb7c553da52205e2.png\")
.<\/span>
\n
\n
\n2.8<\/b> Find the smallest possible length of a simple closed polyline that has at least one common point with each face of the unit cube.
\n
\n
\n3.1<\/b> Six circles have a common interior point. Prove that the center of one of them lies inside the other.
\n
\n
\n3.3<\/b> An arbitrary point is taken inside the regular hexagon ![\"$ABCDEF$\"](\"\/\/latex.artofproblemsolving.com\/8\/0\/2\/8029902caf855d940e465d04ff40101d8850c3e0.png\")
.<\/span> Prove that it is possible to form a hexagon from the segments ![\"$MA$\"](\"\/\/latex.artofproblemsolving.com\/6\/2\/f\/62f7eb82948ac9d7e8659abb37508b1015d8a3cf.png\")
,<\/span> ![\"$MB$\"](\"\/\/latex.artofproblemsolving.com\/8\/5\/6\/856c130e0bb237c3edeb7e3c0246d40cc607e861.png\")
,<\/span> ![\"$MC$\"](\"\/\/latex.artofproblemsolving.com\/4\/d\/5\/4d5ee546f7ea84755eae7a58fbf1d892bd258118.png\")
,<\/span> ![\"$MD$\"](\"\/\/latex.artofproblemsolving.com\/f\/2\/f\/f2f00f55b6b1cf59b8a3b3687a2b9aed8b37578c.png\")
,<\/span> ![\"$ME$\"](\"\/\/latex.artofproblemsolving.com\/d\/1\/a\/d1a30c9c946a561bfb130894432aa55948d58b0d.png\")
,<\/span> ![\"$MF$\"](\"\/\/latex.artofproblemsolving.com\/5\/5\/1\/551fab3023436463570c8159f37571740d523aa7.png\")
,<\/span> the area of which is not less than ![\"$\\frac23$\"](\"\/\/latex.artofproblemsolving.com\/6\/1\/1\/611d08a8c57a214b2b964bba16da8157a5b81c9a.png\")
of the area of the original hexagon.
\n
\n
\n3.5<\/b> Given a triangle,<\/span> all angles of which are expressed in integer degrees and are different from ![\"$45^o$\"](\"\/\/latex.artofproblemsolving.com\/b\/6\/2\/b6209f33ef77435a57e3b1ab0bbe2185e7f26863.png\")
,<\/span> ![\"$90^o$\"](\"\/\/latex.artofproblemsolving.com\/3\/7\/9\/37943786559be7f13b0927b59e138ce1ace0eea6.png\")
,<\/span> ![\"$135^o$\"](\"\/\/latex.artofproblemsolving.com\/a\/d\/e\/ade07d1dcbcdf5109752313df61e920d192ca8c0.png\")
.<\/span> Points ,<\/span> ,<\/span> are the feet of its altitudes, points ![\"$A_2$\"](\"\/\/latex.artofproblemsolving.com\/e\/3\/a\/e3a8ae66ded7f33f9385a37c9cadfb82720013d8.png\")
,<\/span> ![\"$B_2$\"](\"\/\/latex.artofproblemsolving.com\/3\/6\/8\/368b6f971b418d731c62ff2cb59f51c527d22849.png\")
,<\/span> ![\"$C_2$\"](\"\/\/latex.artofproblemsolving.com\/b\/6\/5\/b65e6facfe122c182fe14d503aeace2c52a9739d.png\")
are the feet of the altitudes of triangle ,<\/span> etc. . Prove that there are infinitely many triangles similar to each other.
\n
\n
\n4.2<\/b> The circle with center![\"$O$\"](\"\/\/latex.artofproblemsolving.com\/5\/1\/d\/51da37d984564162c87710ca27bea422f657fb73.png\")
is tangent to the sides of the angle with vertex ![\"$A$\"](\"\/\/latex.artofproblemsolving.com\/0\/1\/9\/019e9892786e493964e145e7c5cf7b700314e53b.png\")
at points and .<\/span> The tangent to the circle intersects line segments ![\"$AK$\"](\"\/\/latex.artofproblemsolving.com\/3\/7\/0\/370334b1a3582d54fad42c735dfdded7d216d3cc.png\")
and ![\"$AM$\"](\"\/\/latex.artofproblemsolving.com\/e\/7\/3\/e73bc78b745edf7fe1e55dbfc3d914190faf5015.png\")
at points ![\"$B$\"](\"\/\/latex.artofproblemsolving.com\/f\/f\/5\/ff5fb3d775862e2123b007eb4373ff6cc1a34d4e.png\")
and ![\"$C$\"](\"\/\/latex.artofproblemsolving.com\/c\/3\/3\/c3355896da590fc491a10150a50416687626d7cc.png\")
,<\/span> respectively, and the line KM intersects line segments ![\"$OB$\"](\"\/\/latex.artofproblemsolving.com\/0\/9\/6\/0964c9cf406ef8e5ec8beaa6a92125f2d8f90460.png\")
and ![\"$OC$\"](\"\/\/latex.artofproblemsolving.com\/2\/0\/f\/20f8f2f1a3ddc6b42fae25a0637e85c747875180.png\")
at points and .<\/span> Prove that the area of triangle ![\"$ODE$\"](\"\/\/latex.artofproblemsolving.com\/a\/d\/f\/adfbfed38bc145be608628b64295119ef073af15.png\")
is equal to a quarter of the area of triangle ![\"$BOC$\"](\"\/\/latex.artofproblemsolving.com\/7\/6\/d\/76d9b534de592b2a7fc63b97e1f0faab799204e9.png\")
if and only if angle A is ![\"$60^o$\"](\"\/\/latex.artofproblemsolving.com\/4\/a\/e\/4ae82fc01ad7a31ae4c8a590a57a1fc4f150d228.png\")
.<\/span>
\n
\n
\n4.3<\/b> In the middle of a round lake there is an island (a convex figure), which is visible from any point on the shore of the lake at an angle of.<\/span> Prove that the island has the shape of a circle.
\n
\n
\n4.5<\/b> Several (finite) sides of the cells of the endless checkered paper are colored red. Once a second, all nodes are selected, each of which has at least two red segments coming out, and all other segments coming out of these nodes are also painted red. Prove that the number of red segments cannot increase indefinitely.
\n
\n
\n
\nPS. You should use hide for answers. Senior Round posted here<\/a>. Collected here<\/a>.","post_canonical":"[b]VI.[\/b] [u]Rounds 1-4[\/u] \n\n\n[b]1.2[\/b] $9$ numbers are written out, the lengths of the angle bisectors, altitudes and medians of a certain triangle. It is known that among them there are no more than $4$ different ones. Prove that this triangle is isosceles.\n\n\n[b]1.3[\/b] Is it possible to cut a cube into 6 equal triangular pyramids?\n\n\n[b]1.6 [\/b] All points of the strip of width 0.001 are colored in two colors. Prove that there are two points of the same color at a distance of 1.\n\n\n[b]1.7[\/b] On sides $BC$, $CA$ and $AB$ of triangle ABC, points $A_1$, $B_1$ and $C_1$ are taken respectively so that $$AC_1:C_1B = BA_1:A_1C = CB_1:B_1A = 2:1$$ Prove that if triangle $A_1B_1C_1$ is equilateral, then triangle $ABC$ is also equilateral.\n\n\n[b]2.5[\/b] On sides $CD$ and $DA$ of parallelogram $ABCD$, points $E$ and $F$ are taken, respectively. Let $K$ be the intersection point of segments $AE$ and $CF$. Prove that if the areas of triangles $AKF$ and $CKE$ are equal, then the point $K$ lies on the diagonal $BD$.\n\n\n[b]2.8[\/b] Find the smallest possible length of a simple closed polyline that has at least one common point with each face of the unit cube.\n\n\n[b]3.1[\/b] Six circles have a common interior point. Prove that the center of one of them lies inside the other.\n\n\n[b]3.3[\/b] An arbitrary point $M$ is taken inside the regular hexagon $ABCDEF$. Prove that it is possible to form a hexagon from the segments $MA$, $MB$, $MC$, $MD$, $ME$, $MF$, the area of \u200b\u200bwhich is not less than $\\frac23$ of the area of \u200b\u200bthe original hexagon.\n\n\n[b]3.5[\/b] Given a triangle $ABC$, all angles of which are expressed in integer degrees and are different from $45^o$, $90^o$, $135^o$. Points $A_1$, $B_1$, $C_1$ are the feet of its altitudes, points $A_2$, $B_2$, $C_2$ are the feet of the altitudes of triangle $A_1B_1C_1$, etc. . Prove that there are infinitely many triangles similar to each other.\n\n\n[b]4.2[\/b] The circle with center $O$ is tangent to the sides of the angle with vertex $A$ at points $K$ and $M$. The tangent to the circle intersects line segments $AK$ and $AM$ at points $B$ and $C$, respectively, and the line KM intersects line segments $OB$ and $OC$ at points $D$ and $E$. Prove that the area of \u200b\u200btriangle $ODE$ is equal to a quarter of the area of \u200b\u200btriangle $BOC$ if and only if angle A is $60^o$.\n\n\n[b]4.3[\/b] In the middle of a round lake there is an island (a convex figure), which is visible from any point on the shore of the lake at an angle of $60^o$. Prove that the island has the shape of a circle.\n\n\n[b]4.5[\/b] Several (finite) sides of the cells of the endless checkered paper are colored red. Once a second, all nodes are selected, each of which has at least two red segments coming out, and all other segments coming out of these nodes are also painted red. Prove that the number of red segments cannot increase indefinitely.\n\n\n\nPS. You should use hide for answers. Senior Round posted [url=https:\/\/artofproblemsolving.com\/community\/c6h2835588p25102426]here[\/url]. Collected [url=https:\/\/artofproblemsolving.com\/community\/c3032551_rfym__geometry]here[\/url].","username":"parmenides51","reported":false,"is_thanked":false,"is_nothanked":false,"attachment":false,"thanks_received":1,"nothanks_received":0,"thankers":"ImSh95","deleted":false,"post_number":1,"post_time":1651355815,"num_edits":8,"post_format":"bbcode","last_edit_time":1653068704,"last_editor_username":"parmenides51","last_edit_reason":"","admin":false,"avatar":"\/\/avatar.artofproblemsolving.com\/avatar_167643.png?t=1472410314","num_posts":18897,"editable":false,"deletable":false,"show_from_start":true,"show_from_end":false}],"topic_id":2835578,"comment_count":2,"num_deleted":0,"topic_title":"Geo from VI Russian Festival of Young Mathematicians 1995 Junior Rounds","target_url":"","target_text":"","topic_type":"forum","state":"none","first_post_id":25102300,"first_poster_id":167643,"first_post_time":1651355815,"first_poster_name":"parmenides51","last_post_time":1653068725,"first_poster_avatar":"\/\/avatar.artofproblemsolving.com\/avatar_167643.png?t=1472410314","last_poster_avatar":"\/\/avatar.artofproblemsolving.com\/avatar_167643.png?t=1472410314","last_post_id":25250206,"last_poster_id":167643,"last_poster_name":"parmenides51","last_update_time":1653068725,"category_id":4,"is_public":true,"roles":{"38516":"mod","242520":"mod","53544":"mod"},"tags":[{"tag_id":48,"tag_text":"geometry","is_visible":true},{"tag_id":1600924,"tag_text":"RFYM","is_visible":true},{"tag_id":146,"tag_text":"3D geometry","is_visible":true},{"tag_id":41772,"tag_text":"combinatorial geometry","is_visible":true},{"tag_id":267,"tag_text":"geometric inequality","is_visible":true}],"can_have_source":false,"locked":false,"forum_locked":0,"announce_type":"none","announce_through":"","announce_factor":0,"preview":"VI.<\/b> Rounds 1-4<\/u>
\n
\n
\n1.2<\/b> numbers are written out, the lengths of the angle bisectors, altitudes and medians of a certain triangle. It is known that among them there are no more than different ones. Prove that this triangle is isosceles.
\n
\n
\n1.3<\/b> Is it possible to cut a cube into 6 equal triangular pyramids?
\n
\n
\n1.6 <\/b> All points of the strip of width 0.001 are colored in two colors. Prove that there are two points of the same color at a distance of 1.
\n
\n
\n1.7<\/b> On sides,<\/span> and of triangle ABC, points ,<\/span> and are taken respectively so that Prove that if triangle is equilateral, then triangle is also equilateral.
\n
\n
\n2.5<\/b> On sides and of parallelogram ,<\/span> points and are taken, respectively. Let be the intersection point of segments and .<\/span> Prove that if the areas of triangles and are equal, then the point lies on the diagonal .<\/span>
\n
\n
\n2.8<\/b> Find the smallest possible length of a simple closed polyline that has at least one common point with each face of the unit cube.
\n
\n
\n3.1<\/b> Six circles have a common interior point. Prove that the center of one of them lies inside the other.
\n
\n
\n3.3<\/b> An arbitrary point is taken inside the regular hexagon .<\/span> Prove that it is possible to form a hexagon from the segments ,<\/span> ,<\/span> ,<\/span> ,<\/span> ,<\/span> ,<\/span> the area of which is not less than of the area of the original hexagon.
\n
\n
\n3.5<\/b> Given a triangle,<\/span> all angles of which are expressed in integer degrees and are different from ,<\/span> ,<\/span> .<\/span> Points ,<\/span> ,<\/span> are the feet of its altitudes, points ,<\/span> ,<\/span> are the feet of the altitudes of triangle ,<\/span> etc. . Prove that there are infinitely many triangles similar to each other.
\n
\n
\n4.2<\/b> The circle with center is tangent to the sides of the angle with vertex at points and .<\/span> The tangent to the circle intersects line segments and at points and ,<\/span> respectively, and the line KM intersects line segments and at points and .<\/span> Prove that the area of triangle is equal to a quarter of the area of triangle if and only if angle A is .<\/span>
\n
\n
\n4.3<\/b> In the middle of a round lake there is an island (a convex figure), which is visible from any point on the shore of the lake at an angle of.<\/span> Prove that the island has the shape of a circle.
\n
\n
\n4.5<\/b> Several (finite) sides of the cells of the endless checkered paper are colored red. Once a second, all nodes are selected, each of which has at least two red segments coming out, and all other segments coming out of these nodes are also painted red. Prove that the number of red segments cannot increase indefinitely.
\n
\n
\n
\nPS. You should use hide for answers. Senior Round posted here<\/a>. Collected here<\/a>.","category_name":"High School Math","category_main_color":"#e75400","category_secondary_color":"#ffe7cc","num_reports":0,"poll_id":0,"source":"","category_num_users":8,"category_num_topics":103885,"category_num_posts":565535,"num_views":106,"cat_can_target":0,"has_thanks":true,"has_nothanks":false,"is_bookmarked":false,"in_feed":false,"is_watched":false},"2848696":{"num_posts":2,"posts_data":[{"post_id":25249323,"topic_id":2848696,"poster_id":167643,"post_rendered":"A number of equilateral triangles are drawn on the plane. They do not intersect, but may have common parts of the sides. We want to color each triangle in some color so that those that touch are colored in different colors (triangles that share the same point can be colored in the same color). Will two colors be enough for such a coloring?","post_canonical":"A number of equilateral triangles are drawn on the plane. They do not intersect, but may have common parts of the sides. We want to color each triangle in some color so that those that touch are colored in different colors (triangles that share the same point can be colored in the same color). Will two colors be enough for such a coloring?","username":"parmenides51","reported":false,"is_thanked":false,"is_nothanked":false,"attachment":false,"thanks_received":0,"nothanks_received":0,"thankers":null,"deleted":false,"post_number":1,"post_time":1653059219,"num_edits":0,"post_format":"bbcode","last_edit_time":0,"last_editor_username":"","last_edit_reason":"","admin":false,"avatar":"\/\/avatar.artofproblemsolving.com\/avatar_167643.png?t=1472410314","num_posts":18897,"editable":false,"deletable":false,"show_from_start":true,"show_from_end":false}],"topic_id":2848696,"comment_count":2,"num_deleted":0,"topic_title":"no of colors to paint some equilateral triangles 1988 Lomonosov Tournament","target_url":"","target_text":"","topic_type":"forum","state":"none","first_post_id":25249323,"first_poster_id":167643,"first_post_time":1653059219,"first_poster_name":"parmenides51","last_post_time":1653067562,"first_poster_avatar":"\/\/avatar.artofproblemsolving.com\/avatar_167643.png?t=1472410314","last_poster_avatar":"\/\/avatar.artofproblemsolving.com\/avatar_238386.png?t=1650777527","last_post_id":25250115,"last_poster_id":238386,"last_poster_name":"ythomashu","last_update_time":1653067562,"category_id":4,"is_public":true,"roles":{"38516":"mod","242520":"mod","53544":"mod"},"tags":[{"tag_id":41772,"tag_text":"combinatorial geometry","is_visible":true},{"tag_id":45241,"tag_text":"Coloring","is_visible":true},{"tag_id":568150,"tag_text":"equilaterals","is_visible":true},{"tag_id":48,"tag_text":"geometry","is_visible":true},{"tag_id":1631859,"tag_text":"Lomonosov Tournament","is_visible":true}],"can_have_source":false,"locked":false,"forum_locked":0,"announce_type":"none","announce_through":"","announce_factor":0,"preview":"A number of equilateral triangles are drawn on the plane. They do not intersect, but may have common parts of the sides. We want to color each triangle in some color so that those that touch are colored in different colors (triangles that share the same point can be colored in the same color). Will two colors be enough for such a coloring?","category_name":"High School Math","category_main_color":"#e75400","category_secondary_color":"#ffe7cc","num_reports":0,"poll_id":0,"source":"","category_num_users":8,"category_num_topics":103885,"category_num_posts":565535,"num_views":51,"cat_can_target":0,"has_thanks":true,"has_nothanks":false,"is_bookmarked":false,"in_feed":false,"is_watched":false}};AoPS.preload_topics[5]={"2848761":{"num_posts":2,"posts_data":[{"post_id":25250138,"topic_id":2848761,"poster_id":208295,"post_rendered":"Title says it all really. Planning on grinding over the summer for AIME qual after not doing the AMC 10. I know I should do the former tests and mocks and study through all the books, but one of my main questions is how much Alcumus per day should I do, and what study things are available outside mocks and Alcumus? I've taken all of the AoPS courses in the past up to Calc, so review should be a lot easier as I already know things.","post_canonical":"Title says it all really. Planning on grinding over the summer for AIME qual after not doing the AMC 10. I know I should do the former tests and mocks and study through all the books, but one of my main questions is how much Alcumus per day should I do, and what study things are available outside mocks and Alcumus? I've taken all of the AoPS courses in the past up to Calc, so review should be a lot easier as I already know things.","username":"moab33","reported":false,"is_thanked":false,"is_nothanked":false,"attachment":false,"thanks_received":0,"nothanks_received":0,"thankers":null,"deleted":false,"post_number":1,"post_time":1653067852,"num_edits":0,"post_format":"bbcode","last_edit_time":0,"last_editor_username":"","last_edit_reason":"","admin":false,"avatar":"\/\/avatar.artofproblemsolving.com\/avatar_208295.png?t=1629751514","num_posts":2123,"editable":false,"deletable":false,"show_from_start":true,"show_from_end":false}],"topic_id":2848761,"comment_count":2,"num_deleted":0,"topic_title":"How to study for AMC 10 effectively?","target_url":"","target_text":"","topic_type":"forum","state":"none","first_post_id":25250138,"first_poster_id":208295,"first_post_time":1653067852,"first_poster_name":"moab33","last_post_time":1653069488,"first_poster_avatar":"\/\/avatar.artofproblemsolving.com\/avatar_208295.png?t=1629751514","last_poster_avatar":"\/\/avatar.artofproblemsolving.com\/avatar_492779.png","last_post_id":25250271,"last_poster_id":492779,"last_poster_name":"buddy2007","last_update_time":1653069488,"category_id":5,"is_public":true,"roles":{"53544":"mod","93494":"mod","86424":"mod","1662":"mod","38516":"mod","242520":"mod","159507":"mod","565384":"mod"},"tags":[{"tag_id":69960,"tag_text":"study","is_visible":true}],"can_have_source":true,"locked":false,"forum_locked":0,"announce_type":"none","announce_through":"","announce_factor":0,"preview":"Title says it all really. Planning on grinding over the summer for AIME qual after not doing the AMC 10. I know I should do the former tests and mocks and study through all the books, but one of my main questions is how much Alcumus per day should I do, and what study things are available outside mocks and Alcumus? I've taken all of the AoPS courses in the past up to Calc, so review should be a lot easier as I already know things.","category_name":"Contests & Programs","category_main_color":"#008fd5","category_secondary_color":"#d9effd","num_reports":0,"poll_id":0,"source":"","category_num_users":7,"category_num_topics":29049,"category_num_posts":471543,"num_views":29,"cat_can_target":0,"has_thanks":true,"has_nothanks":false,"is_bookmarked":false,"in_feed":false,"is_watched":false},"2848336":{"num_posts":4,"posts_data":[{"post_id":25245216,"topic_id":2848336,"poster_id":953304,"post_rendered":"How much does attending the ross summer camp improve chances for getting into mit primes?
\n
\nAlso, I heard that you have to know some linear algebra for the pset. Is hefferson's linear algebra textbook good enough for this? Also are there any other areas outside of a standard high school curriculum that should be learned before trying the pset?
\n
\nFinally, are the problems similar to competition problems, are more like research? For example, would they be more similar to the Ross psets, or more like olympiad problems?","post_canonical":"How much does attending the ross summer camp improve chances for getting into mit primes?\n\nAlso, I heard that you have to know some linear algebra for the pset. Is hefferson's linear algebra textbook good enough for this? Also are there any other areas outside of a standard high school curriculum that should be learned before trying the pset?\n\nFinally, are the problems similar to competition problems, are more like research? For example, would they be more similar to the Ross psets, or more like olympiad problems?","username":"math4life2023","reported":false,"is_thanked":false,"is_nothanked":false,"attachment":false,"thanks_received":1,"nothanks_received":0,"thankers":"ImSh95","deleted":false,"post_number":1,"post_time":1652999786,"num_edits":0,"post_format":"bbcode","last_edit_time":0,"last_editor_username":"","last_edit_reason":"","admin":false,"avatar":"\/\/avatar.artofproblemsolving.com\/avatar_953304.png","num_posts":2,"editable":false,"deletable":false,"show_from_start":true,"show_from_end":false}],"topic_id":2848336,"comment_count":4,"num_deleted":0,"topic_title":"Ross boost for mit primes?","target_url":"","target_text":"","topic_type":"forum","state":"none","first_post_id":25245216,"first_poster_id":953304,"first_post_time":1652999786,"first_poster_name":"math4life2023","last_post_time":1653063788,"first_poster_avatar":"\/\/avatar.artofproblemsolving.com\/avatar_953304.png","last_poster_avatar":"\/\/avatar.artofproblemsolving.com\/avatar_584480.png","last_post_id":25249758,"last_poster_id":584480,"last_poster_name":"CircleInvert","last_update_time":1653063788,"category_id":5,"is_public":true,"roles":{"53544":"mod","93494":"mod","86424":"mod","1662":"mod","38516":"mod","242520":"mod","159507":"mod","565384":"mod"},"tags":[{"tag_id":84,"tag_text":"Ross Mathematics Program","is_visible":true},{"tag_id":135,"tag_text":"MIT","is_visible":true},{"tag_id":209,"tag_text":"college","is_visible":true},{"tag_id":290,"tag_text":"linear algebra","is_visible":true},{"tag_id":48,"tag_text":"geometry","is_visible":true}],"can_have_source":true,"locked":false,"forum_locked":0,"announce_type":"none","announce_through":"","announce_factor":0,"preview":"How much does attending the ross summer camp improve chances for getting into mit primes?
\n
\nAlso, I heard that you have to know some linear algebra for the pset. Is hefferson's linear algebra textbook good enough for this? Also are there any other areas outside of a standard high school curriculum that should be learned before trying the pset?
\n
\nFinally, are the problems similar to competition problems, are more like research? For example, would they be more similar to the Ross psets, or more like olympiad problems?","category_name":"Contests & Programs","category_main_color":"#008fd5","category_secondary_color":"#d9effd","num_reports":0,"poll_id":0,"source":"","category_num_users":7,"category_num_topics":29049,"category_num_posts":471543,"num_views":433,"cat_can_target":0,"has_thanks":true,"has_nothanks":false,"is_bookmarked":false,"in_feed":false,"is_watched":false},"2837951":{"num_posts":113,"posts_data":[{"post_id":25130022,"topic_id":2837951,"poster_id":311064,"post_rendered":"After a long wait we\u2019re back and better than ever!
\n
\nHello to all creative problem solvers,
\n<\/span>
\nDo you want to work on a fun, untimed team math competition with amazing questions?
\n
\nDo you want to have a chance (just by taking a test!) to win prizes?
\n
\nAfter more than a year and thousands of hours of hard work, the OMMC staff<\/span>
,<\/span> where there are '<\/span>s in the exponentiation tower. for example, <\/div>","category_name":"Middle School Math","category_main_color":"#f90","category_secondary_color":"#fff5d4","num_reports":0,"poll_id":0,"source":"","category_num_users":13,"category_num_topics":46945,"category_num_posts":659603,"num_views":2146,"cat_can_target":0,"has_thanks":true,"has_nothanks":false,"is_bookmarked":false,"in_feed":false,"is_watched":false},"2847200":{"num_posts":77,"posts_data":[{"post_id":25233412,"topic_id":2847200,"poster_id":623822,"post_rendered":"Choose the option that is closest","post_canonical":"Choose the option that is closest","username":"URcurious2","reported":false,"is_thanked":false,"is_nothanked":false,"attachment":false,"thanks_received":2,"nothanks_received":0,"thankers":"ImSh95, At777","deleted":false,"post_number":1,"post_time":1652854411,"num_edits":0,"post_format":"bbcode","last_edit_time":0,"last_editor_username":"","last_edit_reason":"","admin":false,"avatar":"\/\/avatar.artofproblemsolving.com\/avatar_623822.png?t=1610748309","num_posts":117,"editable":false,"deletable":false,"show_from_start":true,"show_from_end":false}],"topic_id":2847200,"comment_count":77,"num_deleted":2,"topic_title":"AIME to MathCounts ratio","target_url":"","target_text":"","topic_type":"forum","state":"none","first_post_id":25233412,"first_poster_id":623822,"first_post_time":1652854411,"first_poster_name":"URcurious2","last_post_time":1653070161,"first_poster_avatar":"\/\/avatar.artofproblemsolving.com\/avatar_623822.png?t=1610748309","last_poster_avatar":"\/\/avatar.artofproblemsolving.com\/avatar_775860.png?t=1647808405","last_post_id":25250340,"last_poster_id":775860,"last_poster_name":"Inaaya","last_update_time":1653070161,"category_id":3,"is_public":true,"roles":{"38516":"mod","53544":"mod","242520":"mod"},"tags":[{"tag_id":3,"tag_text":"AMC","is_visible":true},{"tag_id":183,"tag_text":"AIME","is_visible":true},{"tag_id":259,"tag_text":"ratio","is_visible":true},{"tag_id":29911,"tag_text":"poll","is_visible":true}],"can_have_source":false,"locked":false,"forum_locked":0,"announce_type":"none","announce_through":"","announce_factor":0,"preview":"Choose the option that is closest","category_name":"Middle School Math","category_main_color":"#f90","category_secondary_color":"#fff5d4","num_reports":0,"poll_id":47117,"source":"","category_num_users":13,"category_num_topics":46945,"category_num_posts":659603,"num_views":1850,"cat_can_target":0,"has_thanks":true,"has_nothanks":false,"is_bookmarked":false,"in_feed":false,"is_watched":false}};AoPS.preload_topics[4]={"2844078":{"num_posts":4,"posts_data":[{"post_id":25198764,"topic_id":2844078,"poster_id":244795,"post_rendered":"How many the number of arrangements of the letters AAAABBBC in which either the A's appear together in a block of four letters or the B's appear together in a block of three letters?\n
\nCould you tell the answer and the explanation?","post_canonical":"How many the number of arrangements of the letters AAAABBBC in which either the A's appear together in a block of four letters or the B's appear together in a block of three letters?\n\nCould you tell the answer and the explanation?","username":"bsming","reported":false,"is_thanked":false,"is_nothanked":false,"attachment":false,"thanks_received":1,"nothanks_received":0,"thankers":"ImSh95","deleted":false,"post_number":1,"post_time":1652436811,"num_edits":0,"post_format":"bbcode","last_edit_time":0,"last_editor_username":"","last_edit_reason":"","admin":false,"avatar":"\/\/avatar.artofproblemsolving.com\/avatar_244795.png","num_posts":35,"editable":false,"deletable":false,"show_from_start":true,"show_from_end":false}],"topic_id":2844078,"comment_count":4,"num_deleted":0,"topic_title":"arrangements of the letters AAAABBBC","target_url":"","target_text":"","topic_type":"forum","state":"none","first_post_id":25198764,"first_poster_id":244795,"first_post_time":1652436811,"first_poster_name":"bsming","last_post_time":1653069633,"first_poster_avatar":"\/\/avatar.artofproblemsolving.com\/avatar_244795.png","last_poster_avatar":"\/\/avatar.artofproblemsolving.com\/avatar_1313.png","last_post_id":25250283,"last_poster_id":1313,"last_poster_name":"gauss202","last_update_time":1653069633,"category_id":4,"is_public":true,"roles":{"38516":"mod","242520":"mod","53544":"mod"},"tags":[{"tag_id":139072,"tag_text":"MATHCOUNTS prep","is_visible":true}],"can_have_source":false,"locked":false,"forum_locked":0,"announce_type":"none","announce_through":"","announce_factor":0,"preview":"How many the number of arrangements of the letters AAAABBBC in which either the A's appear together in a block of four letters or the B's appear together in a block of three letters?
\n
\nCould you tell the answer and the explanation?","category_name":"High School Math","category_main_color":"#e75400","category_secondary_color":"#ffe7cc","num_reports":0,"poll_id":0,"source":"","category_num_users":8,"category_num_topics":103885,"category_num_posts":565535,"num_views":235,"cat_can_target":0,"has_thanks":true,"has_nothanks":false,"is_bookmarked":false,"in_feed":false,"is_watched":false},"2848183":{"num_posts":2,"posts_data":[{"post_id":25243640,"topic_id":2848183,"poster_id":167643,"post_rendered":"In triangle
with angles and on segment ,<\/span> a point is chosen such that and is the midpoint of segment .<\/span> Find .<\/span>","post_canonical":"In triangle $ABC$ with angles $\\angle ACB = 40^o$ and $\\angle BAC = 60^o$ on segment $BC$, a point $D$ is chosen such that $2 \\cdot CD = AB$ and $M$ is the midpoint of segment $AC$. Find $\\angle CMD$.","username":"parmenides51","reported":false,"is_thanked":false,"is_nothanked":false,"attachment":false,"thanks_received":0,"nothanks_received":0,"thankers":null,"deleted":false,"post_number":1,"post_time":1652986328,"num_edits":0,"post_format":"bbcode","last_edit_time":0,"last_editor_username":"","last_edit_reason":"","admin":false,"avatar":"\/\/avatar.artofproblemsolving.com\/avatar_167643.png?t=1472410314","num_posts":18897,"editable":false,"deletable":false,"show_from_start":true,"show_from_end":false}],"topic_id":2848183,"comment_count":2,"num_deleted":0,"topic_title":"<CMD=? 100-60-40 triangle, 2CD=AB 2022 Russian Young Mathematician 6-7.8","target_url":"","target_text":"","topic_type":"forum","state":"none","first_post_id":25243640,"first_poster_id":167643,"first_post_time":1652986328,"first_poster_name":"parmenides51","last_post_time":1653069099,"first_poster_avatar":"\/\/avatar.artofproblemsolving.com\/avatar_167643.png?t=1472410314","last_poster_avatar":"\/\/avatar.artofproblemsolving.com\/avatar_36948.jpg","last_post_id":25250239,"last_poster_id":36948,"last_poster_name":"sunken rock","last_update_time":1653069099,"category_id":4,"is_public":true,"roles":{"38516":"mod","242520":"mod","53544":"mod"},"tags":[{"tag_id":48,"tag_text":"geometry","is_visible":true},{"tag_id":45165,"tag_text":"angles","is_visible":true},{"tag_id":1629561,"tag_text":"Young Mathematician","is_visible":true}],"can_have_source":false,"locked":false,"forum_locked":0,"announce_type":"none","announce_through":"","announce_factor":0,"preview":"In triangle with angles and on segment ,<\/span> a point is chosen such that and is the midpoint of segment .<\/span> Find .<\/span>","category_name":"High School Math","category_main_color":"#e75400","category_secondary_color":"#ffe7cc","num_reports":0,"poll_id":0,"source":"","category_num_users":8,"category_num_topics":103885,"category_num_posts":565535,"num_views":59,"cat_can_target":0,"has_thanks":true,"has_nothanks":false,"is_bookmarked":false,"in_feed":false,"is_watched":false},"2835578":{"num_posts":2,"posts_data":[{"post_id":25102300,"topic_id":2835578,"poster_id":167643,"post_rendered":"VI.<\/b> Rounds 1-4<\/u>\n
\n
\n1.2<\/b>
numbers are written out, the lengths of the angle bisectors, altitudes and medians of a certain triangle. It is known that among them there are no more than different ones. Prove that this triangle is isosceles.\n
\n
\n1.3<\/b> Is it possible to cut a cube into 6 equal triangular pyramids?
\n
\n
\n1.6 <\/b> All points of the strip of width 0.001 are colored in two colors. Prove that there are two points of the same color at a distance of 1.
\n
\n
\n1.7<\/b> On sides
,<\/span> and of triangle ABC, points ,<\/span> and are taken respectively so that Prove that if triangle is equilateral, then triangle is also equilateral.\n
\n
\n2.5<\/b> On sides
and of parallelogram ,<\/span> points and are taken, respectively. Let be the intersection point of segments and .<\/span> Prove that if the areas of triangles and are equal, then the point lies on the diagonal .<\/span>\n
\n
\n2.8<\/b> Find the smallest possible length of a simple closed polyline that has at least one common point with each face of the unit cube.
\n
\n
\n3.1<\/b> Six circles have a common interior point. Prove that the center of one of them lies inside the other.
\n
\n
\n3.3<\/b> An arbitrary point
is taken inside the regular hexagon .<\/span> Prove that it is possible to form a hexagon from the segments ,<\/span> ,<\/span> ,<\/span> ,<\/span> ,<\/span> ,<\/span> the area of which is not less than of the area of the original hexagon.\n
\n
\n3.5<\/b> Given a triangle
,<\/span> all angles of which are expressed in integer degrees and are different from ,<\/span> ,<\/span> .<\/span> Points ,<\/span> ,<\/span> are the feet of its altitudes, points ,<\/span> ,<\/span> are the feet of the altitudes of triangle ,<\/span> etc. . Prove that there are infinitely many triangles similar to each other.\n
\n
\n4.2<\/b> The circle with center
is tangent to the sides of the angle with vertex at points and .<\/span> The tangent to the circle intersects line segments and at points and ,<\/span> respectively, and the line KM intersects line segments and at points and .<\/span> Prove that the area of triangle is equal to a quarter of the area of triangle if and only if angle A is .<\/span>\n
\n
\n4.3<\/b> In the middle of a round lake there is an island (a convex figure), which is visible from any point on the shore of the lake at an angle of
.<\/span> Prove that the island has the shape of a circle.\n
\n
\n4.5<\/b> Several (finite) sides of the cells of the endless checkered paper are colored red. Once a second, all nodes are selected, each of which has at least two red segments coming out, and all other segments coming out of these nodes are also painted red. Prove that the number of red segments cannot increase indefinitely.
\n
\n
\n
\nPS. You should use hide for answers. Senior Round posted here<\/a>. Collected here<\/a>.","post_canonical":"[b]VI.[\/b] [u]Rounds 1-4[\/u] \n\n\n[b]1.2[\/b] $9$ numbers are written out, the lengths of the angle bisectors, altitudes and medians of a certain triangle. It is known that among them there are no more than $4$ different ones. Prove that this triangle is isosceles.\n\n\n[b]1.3[\/b] Is it possible to cut a cube into 6 equal triangular pyramids?\n\n\n[b]1.6 [\/b] All points of the strip of width 0.001 are colored in two colors. Prove that there are two points of the same color at a distance of 1.\n\n\n[b]1.7[\/b] On sides $BC$, $CA$ and $AB$ of triangle ABC, points $A_1$, $B_1$ and $C_1$ are taken respectively so that $$AC_1:C_1B = BA_1:A_1C = CB_1:B_1A = 2:1$$ Prove that if triangle $A_1B_1C_1$ is equilateral, then triangle $ABC$ is also equilateral.\n\n\n[b]2.5[\/b] On sides $CD$ and $DA$ of parallelogram $ABCD$, points $E$ and $F$ are taken, respectively. Let $K$ be the intersection point of segments $AE$ and $CF$. Prove that if the areas of triangles $AKF$ and $CKE$ are equal, then the point $K$ lies on the diagonal $BD$.\n\n\n[b]2.8[\/b] Find the smallest possible length of a simple closed polyline that has at least one common point with each face of the unit cube.\n\n\n[b]3.1[\/b] Six circles have a common interior point. Prove that the center of one of them lies inside the other.\n\n\n[b]3.3[\/b] An arbitrary point $M$ is taken inside the regular hexagon $ABCDEF$. Prove that it is possible to form a hexagon from the segments $MA$, $MB$, $MC$, $MD$, $ME$, $MF$, the area of \u200b\u200bwhich is not less than $\\frac23$ of the area of \u200b\u200bthe original hexagon.\n\n\n[b]3.5[\/b] Given a triangle $ABC$, all angles of which are expressed in integer degrees and are different from $45^o$, $90^o$, $135^o$. Points $A_1$, $B_1$, $C_1$ are the feet of its altitudes, points $A_2$, $B_2$, $C_2$ are the feet of the altitudes of triangle $A_1B_1C_1$, etc. . Prove that there are infinitely many triangles similar to each other.\n\n\n[b]4.2[\/b] The circle with center $O$ is tangent to the sides of the angle with vertex $A$ at points $K$ and $M$. The tangent to the circle intersects line segments $AK$ and $AM$ at points $B$ and $C$, respectively, and the line KM intersects line segments $OB$ and $OC$ at points $D$ and $E$. Prove that the area of \u200b\u200btriangle $ODE$ is equal to a quarter of the area of \u200b\u200btriangle $BOC$ if and only if angle A is $60^o$.\n\n\n[b]4.3[\/b] In the middle of a round lake there is an island (a convex figure), which is visible from any point on the shore of the lake at an angle of $60^o$. Prove that the island has the shape of a circle.\n\n\n[b]4.5[\/b] Several (finite) sides of the cells of the endless checkered paper are colored red. Once a second, all nodes are selected, each of which has at least two red segments coming out, and all other segments coming out of these nodes are also painted red. Prove that the number of red segments cannot increase indefinitely.\n\n\n\nPS. You should use hide for answers. Senior Round posted [url=https:\/\/artofproblemsolving.com\/community\/c6h2835588p25102426]here[\/url]. Collected [url=https:\/\/artofproblemsolving.com\/community\/c3032551_rfym__geometry]here[\/url].","username":"parmenides51","reported":false,"is_thanked":false,"is_nothanked":false,"attachment":false,"thanks_received":1,"nothanks_received":0,"thankers":"ImSh95","deleted":false,"post_number":1,"post_time":1651355815,"num_edits":8,"post_format":"bbcode","last_edit_time":1653068704,"last_editor_username":"parmenides51","last_edit_reason":"","admin":false,"avatar":"\/\/avatar.artofproblemsolving.com\/avatar_167643.png?t=1472410314","num_posts":18897,"editable":false,"deletable":false,"show_from_start":true,"show_from_end":false}],"topic_id":2835578,"comment_count":2,"num_deleted":0,"topic_title":"Geo from VI Russian Festival of Young Mathematicians 1995 Junior Rounds","target_url":"","target_text":"","topic_type":"forum","state":"none","first_post_id":25102300,"first_poster_id":167643,"first_post_time":1651355815,"first_poster_name":"parmenides51","last_post_time":1653068725,"first_poster_avatar":"\/\/avatar.artofproblemsolving.com\/avatar_167643.png?t=1472410314","last_poster_avatar":"\/\/avatar.artofproblemsolving.com\/avatar_167643.png?t=1472410314","last_post_id":25250206,"last_poster_id":167643,"last_poster_name":"parmenides51","last_update_time":1653068725,"category_id":4,"is_public":true,"roles":{"38516":"mod","242520":"mod","53544":"mod"},"tags":[{"tag_id":48,"tag_text":"geometry","is_visible":true},{"tag_id":1600924,"tag_text":"RFYM","is_visible":true},{"tag_id":146,"tag_text":"3D geometry","is_visible":true},{"tag_id":41772,"tag_text":"combinatorial geometry","is_visible":true},{"tag_id":267,"tag_text":"geometric inequality","is_visible":true}],"can_have_source":false,"locked":false,"forum_locked":0,"announce_type":"none","announce_through":"","announce_factor":0,"preview":"VI.<\/b> Rounds 1-4<\/u>
\n
\n
\n1.2<\/b>
numbers are written out, the lengths of the angle bisectors, altitudes and medians of a certain triangle. It is known that among them there are no more than different ones. Prove that this triangle is isosceles.\n
\n
\n1.3<\/b> Is it possible to cut a cube into 6 equal triangular pyramids?
\n
\n
\n1.6 <\/b> All points of the strip of width 0.001 are colored in two colors. Prove that there are two points of the same color at a distance of 1.
\n
\n
\n1.7<\/b> On sides
,<\/span> and of triangle ABC, points ,<\/span> and are taken respectively so that Prove that if triangle is equilateral, then triangle is also equilateral.\n
\n
\n2.5<\/b> On sides
and of parallelogram ,<\/span> points and are taken, respectively. Let be the intersection point of segments and .<\/span> Prove that if the areas of triangles and are equal, then the point lies on the diagonal .<\/span>\n
\n
\n2.8<\/b> Find the smallest possible length of a simple closed polyline that has at least one common point with each face of the unit cube.
\n
\n
\n3.1<\/b> Six circles have a common interior point. Prove that the center of one of them lies inside the other.
\n
\n
\n3.3<\/b> An arbitrary point
is taken inside the regular hexagon .<\/span> Prove that it is possible to form a hexagon from the segments ,<\/span> ,<\/span> ,<\/span> ,<\/span> ,<\/span> ,<\/span> the area of which is not less than of the area of the original hexagon.\n
\n
\n3.5<\/b> Given a triangle
,<\/span> all angles of which are expressed in integer degrees and are different from ,<\/span> ,<\/span> .<\/span> Points ,<\/span> ,<\/span> are the feet of its altitudes, points ,<\/span> ,<\/span> are the feet of the altitudes of triangle ,<\/span> etc. . Prove that there are infinitely many triangles similar to each other.\n
\n
\n4.2<\/b> The circle with center
is tangent to the sides of the angle with vertex at points and .<\/span> The tangent to the circle intersects line segments and at points and ,<\/span> respectively, and the line KM intersects line segments and at points and .<\/span> Prove that the area of triangle is equal to a quarter of the area of triangle if and only if angle A is .<\/span>\n
\n
\n4.3<\/b> In the middle of a round lake there is an island (a convex figure), which is visible from any point on the shore of the lake at an angle of
.<\/span> Prove that the island has the shape of a circle.\n
\n
\n4.5<\/b> Several (finite) sides of the cells of the endless checkered paper are colored red. Once a second, all nodes are selected, each of which has at least two red segments coming out, and all other segments coming out of these nodes are also painted red. Prove that the number of red segments cannot increase indefinitely.
\n
\n
\n
\nPS. You should use hide for answers. Senior Round posted here<\/a>. Collected here<\/a>.","category_name":"High School Math","category_main_color":"#e75400","category_secondary_color":"#ffe7cc","num_reports":0,"poll_id":0,"source":"","category_num_users":8,"category_num_topics":103885,"category_num_posts":565535,"num_views":106,"cat_can_target":0,"has_thanks":true,"has_nothanks":false,"is_bookmarked":false,"in_feed":false,"is_watched":false},"2848696":{"num_posts":2,"posts_data":[{"post_id":25249323,"topic_id":2848696,"poster_id":167643,"post_rendered":"A number of equilateral triangles are drawn on the plane. They do not intersect, but may have common parts of the sides. We want to color each triangle in some color so that those that touch are colored in different colors (triangles that share the same point can be colored in the same color). Will two colors be enough for such a coloring?","post_canonical":"A number of equilateral triangles are drawn on the plane. They do not intersect, but may have common parts of the sides. We want to color each triangle in some color so that those that touch are colored in different colors (triangles that share the same point can be colored in the same color). Will two colors be enough for such a coloring?","username":"parmenides51","reported":false,"is_thanked":false,"is_nothanked":false,"attachment":false,"thanks_received":0,"nothanks_received":0,"thankers":null,"deleted":false,"post_number":1,"post_time":1653059219,"num_edits":0,"post_format":"bbcode","last_edit_time":0,"last_editor_username":"","last_edit_reason":"","admin":false,"avatar":"\/\/avatar.artofproblemsolving.com\/avatar_167643.png?t=1472410314","num_posts":18897,"editable":false,"deletable":false,"show_from_start":true,"show_from_end":false}],"topic_id":2848696,"comment_count":2,"num_deleted":0,"topic_title":"no of colors to paint some equilateral triangles 1988 Lomonosov Tournament","target_url":"","target_text":"","topic_type":"forum","state":"none","first_post_id":25249323,"first_poster_id":167643,"first_post_time":1653059219,"first_poster_name":"parmenides51","last_post_time":1653067562,"first_poster_avatar":"\/\/avatar.artofproblemsolving.com\/avatar_167643.png?t=1472410314","last_poster_avatar":"\/\/avatar.artofproblemsolving.com\/avatar_238386.png?t=1650777527","last_post_id":25250115,"last_poster_id":238386,"last_poster_name":"ythomashu","last_update_time":1653067562,"category_id":4,"is_public":true,"roles":{"38516":"mod","242520":"mod","53544":"mod"},"tags":[{"tag_id":41772,"tag_text":"combinatorial geometry","is_visible":true},{"tag_id":45241,"tag_text":"Coloring","is_visible":true},{"tag_id":568150,"tag_text":"equilaterals","is_visible":true},{"tag_id":48,"tag_text":"geometry","is_visible":true},{"tag_id":1631859,"tag_text":"Lomonosov Tournament","is_visible":true}],"can_have_source":false,"locked":false,"forum_locked":0,"announce_type":"none","announce_through":"","announce_factor":0,"preview":"A number of equilateral triangles are drawn on the plane. They do not intersect, but may have common parts of the sides. We want to color each triangle in some color so that those that touch are colored in different colors (triangles that share the same point can be colored in the same color). Will two colors be enough for such a coloring?","category_name":"High School Math","category_main_color":"#e75400","category_secondary_color":"#ffe7cc","num_reports":0,"poll_id":0,"source":"","category_num_users":8,"category_num_topics":103885,"category_num_posts":565535,"num_views":51,"cat_can_target":0,"has_thanks":true,"has_nothanks":false,"is_bookmarked":false,"in_feed":false,"is_watched":false}};AoPS.preload_topics[5]={"2848761":{"num_posts":2,"posts_data":[{"post_id":25250138,"topic_id":2848761,"poster_id":208295,"post_rendered":"Title says it all really. Planning on grinding over the summer for AIME qual after not doing the AMC 10. I know I should do the former tests and mocks and study through all the books, but one of my main questions is how much Alcumus per day should I do, and what study things are available outside mocks and Alcumus? I've taken all of the AoPS courses in the past up to Calc, so review should be a lot easier as I already know things.","post_canonical":"Title says it all really. Planning on grinding over the summer for AIME qual after not doing the AMC 10. I know I should do the former tests and mocks and study through all the books, but one of my main questions is how much Alcumus per day should I do, and what study things are available outside mocks and Alcumus? I've taken all of the AoPS courses in the past up to Calc, so review should be a lot easier as I already know things.","username":"moab33","reported":false,"is_thanked":false,"is_nothanked":false,"attachment":false,"thanks_received":0,"nothanks_received":0,"thankers":null,"deleted":false,"post_number":1,"post_time":1653067852,"num_edits":0,"post_format":"bbcode","last_edit_time":0,"last_editor_username":"","last_edit_reason":"","admin":false,"avatar":"\/\/avatar.artofproblemsolving.com\/avatar_208295.png?t=1629751514","num_posts":2123,"editable":false,"deletable":false,"show_from_start":true,"show_from_end":false}],"topic_id":2848761,"comment_count":2,"num_deleted":0,"topic_title":"How to study for AMC 10 effectively?","target_url":"","target_text":"","topic_type":"forum","state":"none","first_post_id":25250138,"first_poster_id":208295,"first_post_time":1653067852,"first_poster_name":"moab33","last_post_time":1653069488,"first_poster_avatar":"\/\/avatar.artofproblemsolving.com\/avatar_208295.png?t=1629751514","last_poster_avatar":"\/\/avatar.artofproblemsolving.com\/avatar_492779.png","last_post_id":25250271,"last_poster_id":492779,"last_poster_name":"buddy2007","last_update_time":1653069488,"category_id":5,"is_public":true,"roles":{"53544":"mod","93494":"mod","86424":"mod","1662":"mod","38516":"mod","242520":"mod","159507":"mod","565384":"mod"},"tags":[{"tag_id":69960,"tag_text":"study","is_visible":true}],"can_have_source":true,"locked":false,"forum_locked":0,"announce_type":"none","announce_through":"","announce_factor":0,"preview":"Title says it all really. Planning on grinding over the summer for AIME qual after not doing the AMC 10. I know I should do the former tests and mocks and study through all the books, but one of my main questions is how much Alcumus per day should I do, and what study things are available outside mocks and Alcumus? I've taken all of the AoPS courses in the past up to Calc, so review should be a lot easier as I already know things.","category_name":"Contests & Programs","category_main_color":"#008fd5","category_secondary_color":"#d9effd","num_reports":0,"poll_id":0,"source":"","category_num_users":7,"category_num_topics":29049,"category_num_posts":471543,"num_views":29,"cat_can_target":0,"has_thanks":true,"has_nothanks":false,"is_bookmarked":false,"in_feed":false,"is_watched":false},"2848336":{"num_posts":4,"posts_data":[{"post_id":25245216,"topic_id":2848336,"poster_id":953304,"post_rendered":"How much does attending the ross summer camp improve chances for getting into mit primes?
\n
\nAlso, I heard that you have to know some linear algebra for the pset. Is hefferson's linear algebra textbook good enough for this? Also are there any other areas outside of a standard high school curriculum that should be learned before trying the pset?
\n
\nFinally, are the problems similar to competition problems, are more like research? For example, would they be more similar to the Ross psets, or more like olympiad problems?","post_canonical":"How much does attending the ross summer camp improve chances for getting into mit primes?\n\nAlso, I heard that you have to know some linear algebra for the pset. Is hefferson's linear algebra textbook good enough for this? Also are there any other areas outside of a standard high school curriculum that should be learned before trying the pset?\n\nFinally, are the problems similar to competition problems, are more like research? For example, would they be more similar to the Ross psets, or more like olympiad problems?","username":"math4life2023","reported":false,"is_thanked":false,"is_nothanked":false,"attachment":false,"thanks_received":1,"nothanks_received":0,"thankers":"ImSh95","deleted":false,"post_number":1,"post_time":1652999786,"num_edits":0,"post_format":"bbcode","last_edit_time":0,"last_editor_username":"","last_edit_reason":"","admin":false,"avatar":"\/\/avatar.artofproblemsolving.com\/avatar_953304.png","num_posts":2,"editable":false,"deletable":false,"show_from_start":true,"show_from_end":false}],"topic_id":2848336,"comment_count":4,"num_deleted":0,"topic_title":"Ross boost for mit primes?","target_url":"","target_text":"","topic_type":"forum","state":"none","first_post_id":25245216,"first_poster_id":953304,"first_post_time":1652999786,"first_poster_name":"math4life2023","last_post_time":1653063788,"first_poster_avatar":"\/\/avatar.artofproblemsolving.com\/avatar_953304.png","last_poster_avatar":"\/\/avatar.artofproblemsolving.com\/avatar_584480.png","last_post_id":25249758,"last_poster_id":584480,"last_poster_name":"CircleInvert","last_update_time":1653063788,"category_id":5,"is_public":true,"roles":{"53544":"mod","93494":"mod","86424":"mod","1662":"mod","38516":"mod","242520":"mod","159507":"mod","565384":"mod"},"tags":[{"tag_id":84,"tag_text":"Ross Mathematics Program","is_visible":true},{"tag_id":135,"tag_text":"MIT","is_visible":true},{"tag_id":209,"tag_text":"college","is_visible":true},{"tag_id":290,"tag_text":"linear algebra","is_visible":true},{"tag_id":48,"tag_text":"geometry","is_visible":true}],"can_have_source":true,"locked":false,"forum_locked":0,"announce_type":"none","announce_through":"","announce_factor":0,"preview":"How much does attending the ross summer camp improve chances for getting into mit primes?
\n
\nAlso, I heard that you have to know some linear algebra for the pset. Is hefferson's linear algebra textbook good enough for this? Also are there any other areas outside of a standard high school curriculum that should be learned before trying the pset?
\n
\nFinally, are the problems similar to competition problems, are more like research? For example, would they be more similar to the Ross psets, or more like olympiad problems?","category_name":"Contests & Programs","category_main_color":"#008fd5","category_secondary_color":"#d9effd","num_reports":0,"poll_id":0,"source":"","category_num_users":7,"category_num_topics":29049,"category_num_posts":471543,"num_views":433,"cat_can_target":0,"has_thanks":true,"has_nothanks":false,"is_bookmarked":false,"in_feed":false,"is_watched":false},"2837951":{"num_posts":113,"posts_data":[{"post_id":25130022,"topic_id":2837951,"poster_id":311064,"post_rendered":"After a long wait we\u2019re back and better than ever!
\n
\nHello to all creative problem solvers,
\n<\/span>
\nDo you want to work on a fun, untimed team math competition with amazing questions?
\n
\nDo you want to have a chance (just by taking a test!) to win prizes?
\n
\nAfter more than a year and thousands of hours of hard work, the OMMC staff<\/span>
squareman, billert, TempestGamer327, CatsAway, Penguin_Puddles, naman12, bissue, ike.chen, jacoporizzo, v4913, ApraTrip, bryanguo, nicksms, cj13609517288, vsamc, AP01, Kevnut_937, studentahere, vinay_0606, marmoset, Lemonberry, focus1111, DottedCalculator, sotpidot, JustinLee2017, rocketsri, bradygho, ritwin, RP3.1415, Serena_Xu, YBSuburbanTea<\/div> would like to present to you the
\n
\nOnline Monmouth Math Competition!
\n<\/span>
\n
\nUse the link http:\/\/www.ommcofficial.org\/<\/a> or https:\/\/ommc-website.vercel.app\/<\/a>. Check out our shiny new website with all the important information you need!<\/b>
\n
\nThis is not a local competition; any student 18 or younger anywhere in the world can attend. We have changed some elements of our contest format, so read this announcement carefully and thoroughly! Our website is currently down but we will let you know when it gets back up. Thanks for your understanding!<\/b>
\n
\nYou may have seen our earlier hype announcement<\/a>. We will still be posting on that thread with Problem of the Months and new video releases. But this is where we will post all updates about the competition.
\n
\nWhen is this?
\n<\/b>
\nThe test will be released on May 27th and will be due on June 5th<\/b>, tentatively (10 days to work on it). Mark your calendars!
\n
\nWho runs this?
\n<\/b>
\nThe Online Monmouth Math Competition (OMMC) for short was founded by a school friend (TempestGamer327) as well as myself. Later, a fellow WOOT classmate billert stepped up as well to help manage the competition and arrange a partnership with another student-run STEM educational organization, Buzzonline (buzzonline.org). Together, we are the three OMMC directors and have worked tirelessly to bring this contest to fruition. We also cannot thank our fellow staff members enough for the work and effort they have put into this organization as well. As of now, we also provide a monthly resource via the Problem of the Month, as well as some Youtube content coming soon. You can find some of this on this AoPS thread: https:\/\/artofproblemsolving.com\/community\/c5h2731203<\/a>
\n
\nWhat happened in OMMC Year 1?
\n<\/b>
\nOMMC Year 1 was for the most part a big success! We had 230+ participants from around the world take part in the competition, and the winners came away with hundreds of dollars in prizes! Questions were high quality and the test went smoothly.
\n
\nIs this going to be exactly the same as OMMC Year 2?
\n<\/b>
\nChange is good! We\u2019re dramatically switching things up for OMMC Year 2. We\u2019re going to have one single team round with 25 questions, and teams can be up to 4 people.<\/b> The test is untimed<\/b>: you\u2019re going to have around a week to work on the problems with your team. Most importantly, the questions are just going to be better this time around.
\n
\nHow are the problems?
\n<\/b>
\nOnly the best problems by our panel of dedicated and talented problem writers have been selected. Hundreds of problems have been comprehensively reviewed by our panel of equally wonderful testsolvers. Our content creation staff has achieved pretty much every mathematical achievement possible! Staff members have qualified for AIME, excelled at USAMO and USAJMO, and attended MOP.<\/b> Our staff members have contributed to countless student-led math organizations and competitions<\/b> in the past and we all have a high degree of mathematical experience under our belt. I believe that OMMC Year 2 contains some of our best work yet.
\n
\nHere are sample problems that we encourage prospective contestants to try.
\n
\nhttps:\/\/artofproblemsolving.com\/community\/c2825027<\/a>
\n
\nOr, check out the problems from last year\u2019s contest:
\n
\nhttps:\/\/artofproblemsolving.com\/community\/c1976711<\/a>
\n
\nSome high quality mock contests that have been contributed to by OMMC Staff Members include SADGIME<\/a>, POGIME<\/a>, and AAMC<\/a>. Other contests staff members have contributed heavily to include ADMC<\/a> and OYMC<\/a>.
\n
\nHow hard is it?
\n<\/b>
\nWe have designed the test to be accessible to beginners at the early end but also challenging to experts on the late end. The early questions will be around the difficulty of easy questions from the AMC 10\/12. Later questions will be at or exceeding the difficulty of the hardest questions from the AIME. We hope that teams will collaborate and think deeply about the problems on the test.
\n
\nHow do we sign up?
\n<\/b>
\nYou won\u2019t have to! You\u2019ll just put in your information as you submit the test, since it\u2019s untimed. However, we do encourage you to \u201csign up\u201d on this thread, just like how you might with a mock contest. This isn\u2019t required to take the test nor does it force you to take the test. But it\u2019s a great way to show support for us and bump the thread to the top of the forums, so we do appreciate it!
\n
\nHow will the test be held?
\n<\/b>
\nWe highly recommend competitors join our Community Discord<\/b> for the latest updates on the competition, as well as for finding team members to team up with. However, all the important information will also be updated on this thread as necessary. Each team can consist of between 1 and 4 people, inclusive. Each competitor in a team has to be 18 or younger to be eligible for the competition.<\/b>
\n
\nSolo participants are allowed and will be treated simply as one man teams. They will be eligible for the same prizes as teams with multiple people.
\n
\nOur test will be held completely online and untimed. There will be one single test of 25 questions that all members of the team can access. Each question has a nonnegative integer answer. Each question is weighted equally, so each team will receive a single score out of 25.
\n
\nAs for what is allowed, we do not allow the use of anything other than writing utensils, scratch paper, compass, ruler\/straightedge, and a single four function calculator (addition, subtraction, multiplication, division). In particular, the use of websites such as Wolfram Alpha, Geogebra, Symbolab, and\/or Desmos is not allowed. Competitors can only communicate about the test with the people in their team. Collaboration between teams or between a team and an individual not on the team, is prohibited. If we find any violations of academic integrity, we will disqualify all teams involved.
\n
\nTiebreaker rounds will be given out if necessary after the contest period has ended. We will contact teams through email for this.
\n
\nOn May 27th, we\u2019ll put out a link by which teams can register and access the test. Teams will put in their registration information as they submit the test. For now, we recommend competitors to search for team members and join the OMMC Discord Community for further updates.
\n
\nPrizes?
\n<\/b>
\nPrizes shouldn\u2019t be the main reason someone takes OMMC, but in previous years we have been sponsored by organizations such as AoPS, Maplesoft, and Wolfram Alpha, who have provided hundreds of dollars to top scoring competitors.
\n
\nThis year, we have a 45 dollar Desmos Gift Card Code, 300 dollars in gift cards and T-shirts from Jane Street, a 500 dollar Geogebra Webinar, 100 dollars in AoPS coupons, and 3600 dollars in Wolfram Alpha Notebook Editions to give out so far. We are happy to announce that Maplesoft will be sponsoring us with $168 value in 4 Maple Learn Premium accounts, active for 6 months, that will be given to the winning team. More updates on prizes coming soon. <\/b>
\n
\nSome of these prizes will be raffled out! You just need to put in a submission to be eligible.<\/b> Spread the news and keep the signups going, you do NOT want to miss this opportunity!
\n
\nI have more questions. Who do I ask?
\n<\/b>
\nWe respond most quickly on our community discord, but you can also contact us through email via the ommcofficial@gmail.com address.
\n
\nWe hope for your participation, and good luck!
\n<\/b>
\nsquareman & the OMMC staff","post_canonical":"After a long wait we\u2019re back and better than ever!\n\n[size=200]Hello to all creative problem solvers,\n[\/size]\nDo you want to work on a fun, untimed team math competition with amazing questions?\n\nDo you want to have a chance (just by taking a test!) to win prizes?\n\nAfter more than a year and thousands of hours of hard work, the [hide=OMMC staff]squareman, billert, TempestGamer327, CatsAway, Penguin_Puddles, naman12, bissue, ike.chen, jacoporizzo, v4913, ApraTrip, bryanguo, nicksms, cj13609517288, vsamc, AP01, Kevnut_937, studentahere, vinay_0606, marmoset, Lemonberry, focus1111, DottedCalculator, sotpidot, JustinLee2017, rocketsri, bradygho, ritwin, RP3.1415, Serena_Xu, YBSuburbanTea[\/hide] would like to present to you the \n\n[size=200]Online Monmouth Math Competition!\n[\/size]\n\nUse the link [b][url]http:\/\/www.ommcofficial.org\/[\/url] or [url]https:\/\/ommc-website.vercel.app\/[\/url]. Check out our shiny new website with all the important information you need![\/b]\n\n[b]This is not a local competition; any student 18 or younger anywhere in the world can attend. We have changed some elements of our contest format, so read this announcement carefully and thoroughly! Our website is currently down but we will let you know when it gets back up. Thanks for your understanding![\/b]\n\nYou may have seen our [url=https:\/\/artofproblemsolving.com\/community\/c5h2731203]earlier hype announcement[\/url]. We will still be posting on that thread with Problem of the Months and new video releases. But this is where we will post all updates about the competition.\n\n[b]When is this? \n[\/b]\nThe test will be released on [b]May 27th and will be due on June 5th[\/b], tentatively (10 days to work on it). Mark your calendars!\n\n[b]Who runs this?\n[\/b]\nThe Online Monmouth Math Competition (OMMC) for short was founded by a school friend (TempestGamer327) as well as myself. Later, a fellow WOOT classmate billert stepped up as well to help manage the competition and arrange a partnership with another student-run STEM educational organization, Buzzonline (buzzonline.org). Together, we are the three OMMC directors and have worked tirelessly to bring this contest to fruition. We also cannot thank our fellow staff members enough for the work and effort they have put into this organization as well. As of now, we also provide a monthly resource via the Problem of the Month, as well as some Youtube content coming soon. You can find some of this on this AoPS thread: [url]https:\/\/artofproblemsolving.com\/community\/c5h2731203[\/url]\n\n[b]What happened in OMMC Year 1?\n[\/b]\nOMMC Year 1 was for the most part a big success! We had 230+ participants from around the world take part in the competition, and the winners came away with hundreds of dollars in prizes! Questions were high quality and the test went smoothly. \n\n[b]Is this going to be exactly the same as OMMC Year 2?\n[\/b]\nChange is good! We\u2019re dramatically switching things up for OMMC Year 2. We\u2019re going to have [b]one single team round with 25 questions, and teams can be up to 4 people.[\/b] The test is [b]untimed[\/b]: you\u2019re going to have around a week to work on the problems with your team. Most importantly, the questions are just going to be better this time around. \n\n[b]How are the problems?\n[\/b]\nOnly the best problems by our panel of dedicated and talented problem writers have been selected. Hundreds of problems have been comprehensively reviewed by our panel of equally wonderful testsolvers. Our content creation staff has achieved pretty much every mathematical achievement possible! Staff members have [b]qualified for AIME, excelled at USAMO and USAJMO, and attended MOP.[\/b] Our staff members have contributed to [b]countless student-led math organizations and competitions[\/b] in the past and we all have a high degree of mathematical experience under our belt. I believe that OMMC Year 2 contains some of our best work yet. \n\nHere are sample problems that we encourage prospective contestants to try.\n\n[url]https:\/\/artofproblemsolving.com\/community\/c2825027[\/url]\n\nOr, check out the problems from last year\u2019s contest: \n\n[url]https:\/\/artofproblemsolving.com\/community\/c1976711[\/url]\n\nSome high quality mock contests that have been contributed to by OMMC Staff Members include [url=https:\/\/artofproblemsolving.com\/community\/c594864t183f594864h2550289_sadgime__mock_aime_test_concluded]SADGIME[\/url], [url=https:\/\/artofproblemsolving.com\/community\/c594864t183f594864h2470832_pogime__mock_aime_released]POGIME[\/url], and [url=https:\/\/artofproblemsolving.com\/community\/c594864t183f594864h2690325_aaime_released_aamc_810aime_series]AAMC[\/url]. Other contests staff members have contributed heavily to include [url=https:\/\/artofproblemsolving.com\/community\/q1h2665919p23098559]ADMC[\/url] and [url=https:\/\/artofproblemsolving.com\/community\/q2h2535331p21573474]OYMC[\/url].\n\n[b]How hard is it?\n[\/b]\nWe have designed the test to be accessible to beginners at the early end but also challenging to experts on the late end. The early questions will be around the difficulty of easy questions from the AMC 10\/12. Later questions will be at or exceeding the difficulty of the hardest questions from the AIME. We hope that teams will collaborate and think deeply about the problems on the test.\n\n[b]How do we sign up?\n[\/b]\nYou won\u2019t have to! You\u2019ll just put in your information as you submit the test, since it\u2019s untimed. However, we do encourage you to \u201csign up\u201d on this thread, just like how you might with a mock contest. This isn\u2019t required to take the test nor does it force you to take the test. But it\u2019s a great way to show support for us and bump the thread to the top of the forums, so we do appreciate it!\n\n[b]How will the test be held?\n[\/b]\nWe highly recommend competitors join our [b]Community Discord[\/b] for the latest updates on the competition, as well as for finding team members to team up with. However, all the important information will also be updated on this thread as necessary. [b]Each team can consist of between 1 and 4 people, inclusive. Each competitor in a team has to be 18 or younger to be eligible for the competition.[\/b]\n\nSolo participants are allowed and will be treated simply as one man teams. They will be eligible for the same prizes as teams with multiple people. \n\nOur test will be held completely online and untimed. There will be one single test of 25 questions that all members of the team can access. Each question has a nonnegative integer answer. Each question is weighted equally, so each team will receive a single score out of 25. \n\nAs for what is allowed, we do not allow the use of anything other than writing utensils, scratch paper, compass, ruler\/straightedge, and a single four function calculator (addition, subtraction, multiplication, division). In particular, the use of websites such as Wolfram Alpha, Geogebra, Symbolab, and\/or Desmos is not allowed. Competitors can only communicate about the test with the people in their team. Collaboration between teams or between a team and an individual not on the team, is prohibited. If we find any violations of academic integrity, we will disqualify all teams involved. \n\nTiebreaker rounds will be given out if necessary after the contest period has ended. We will contact teams through email for this. \n\nOn May 27th, we\u2019ll put out a link by which teams can register and access the test. Teams will put in their registration information as they submit the test. For now, we recommend competitors to search for team members and join the OMMC Discord Community for further updates. \n\n[b]Prizes?\n[\/b]\nPrizes shouldn\u2019t be the main reason someone takes OMMC, but in previous years we have been sponsored by organizations such as AoPS, Maplesoft, and Wolfram Alpha, who have provided hundreds of dollars to top scoring competitors. \n\n[b]This year, we have a 45 dollar Desmos Gift Card Code, 300 dollars in gift cards and T-shirts from Jane Street, a 500 dollar Geogebra Webinar, 100 dollars in AoPS coupons, and 3600 dollars in Wolfram Alpha Notebook Editions to give out so far. We are happy to announce that Maplesoft will be sponsoring us with $168 value in 4 Maple Learn Premium accounts, active for 6 months, that will be given to the winning team. More updates on prizes coming soon. [\/b]\n\n[b]Some of these prizes will be raffled out! You just need to put in a submission to be eligible.[\/b] Spread the news and keep the signups going, you do NOT want to miss this opportunity!\n\n[b]I have more questions. Who do I ask?\n[\/b]\nWe respond most quickly on our community discord, but you can also contact us through email via the ommcofficial@gmail.com address.\n\n[b]We hope for your participation, and good luck! \n[\/b]\nsquareman & the OMMC staff","username":"squareman","reported":false,"is_thanked":false,"is_nothanked":false,"attachment":false,"thanks_received":57,"nothanks_received":0,"thankers":"pog, RP3.1415, teasaffrontaffy, Bole, StopSine, Mogmog8, rayfish, Jndd, Bradygho, mahaler, mathleticguyyy, v4913, bissue, JustinLee2017, LemonBerry, rosegold248, vsamc, megarnie, Math4Life2020, ApraTrip, Robomania_534, Catsaway, HamstPan38825, studentahere, AlphaBetaGammaOmega, YBSuburbanTea, bryanguo, cj13609517288, jacoporizzo, CT17, andiesmountain, CyclicISLscelesTrapezoid, rocketsri, TempestGamer237, awesomehuman, rama1728, Ninjasolver0201, megahertz13, ImSh95, son7, Focus1111, ostriches88, billert, skyguy88, russellk, Sross314, GoodMorning, Lamboreghini, Jc426, justJen, centslordm, PlayfulOwl-aops, IMOTC, GoldenOstraprey, crazyeyemoody907, rg_ryse, wxl18","deleted":false,"post_number":1,"post_time":1651623059,"num_edits":17,"post_format":"bbcode","last_edit_time":1652916491,"last_editor_username":"squareman","last_edit_reason":"","admin":false,"avatar":"\/\/avatar.artofproblemsolving.com\/avatar_311064.jpeg?t=1612816163","num_posts":666,"editable":false,"deletable":false,"show_from_start":true,"show_from_end":false}],"topic_id":2837951,"comment_count":113,"num_deleted":8,"topic_title":"[Confirmed $4713+ in Prizes And Counting] OMMC Contest 2022: Back For Year 2!","target_url":"","target_text":"","topic_type":"forum","state":"none","first_post_id":25130022,"first_poster_id":311064,"first_post_time":1651623059,"first_poster_name":"squareman","last_post_time":1653060186,"first_poster_avatar":"\/\/avatar.artofproblemsolving.com\/avatar_311064.jpeg?t=1612816163","last_poster_avatar":"\/\/avatar.artofproblemsolving.com\/avatar_621129.png","last_post_id":25249397,"last_poster_id":621129,"last_poster_name":"fuzimiao2013","last_update_time":1653060186,"category_id":5,"is_public":true,"roles":{"53544":"mod","93494":"mod","86424":"mod","1662":"mod","38516":"mod","242520":"mod","159507":"mod","565384":"mod"},"tags":[{"tag_id":1142827,"tag_text":"ommc","is_visible":true},{"tag_id":30818,"tag_text":"math competition","is_visible":true},{"tag_id":63310,"tag_text":"High school math","is_visible":true},{"tag_id":31581,"tag_text":"Math Competitions","is_visible":true}],"can_have_source":true,"locked":false,"forum_locked":0,"announce_type":"none","announce_through":"","announce_factor":0,"preview":"After a long wait we\u2019re back and better than ever!
\n
\nHello to all creative problem solvers,
\n
\nDo you want to work on a fun, untimed team math competition with amazing questions?
\n
\nDo you want to have a chance (just by taking a test!) to win prizes?
\n
\nAfter more than a year and thousands of hours of hard work, the OMMC staff<\/span>
\n
\nOnline Monmouth Math Competition!
\n<\/span>
\n
\nUse the link http:\/\/www.ommcofficial.org\/<\/a> or https:\/\/ommc-website.vercel.app\/<\/a>. Check out our shiny new website with all the important information you need!<\/b>
\n
\nThis is not a local competition; any student 18 or younger anywhere in the world can attend. We have changed some elements of our contest format, so read this announcement carefully and thoroughly! Our website is currently down but we will let you know when it gets back up. Thanks for your understanding!<\/b>
\n
\nYou may have seen our earlier hype announcement<\/a>. We will still be posting on that thread with Problem of the Months and new video releases. But this is where we will post all updates about the competition.
\n
\nWhen is this?
\n<\/b>
\nThe test will be released on May 27th and will be due on June 5th<\/b>, tentatively (10 days to work on it). Mark your calendars!
\n
\nWho runs this?
\n<\/b>
\nThe Online Monmouth Math Competition (OMMC) for short was founded by a school friend (TempestGamer327) as well as myself. Later, a fellow WOOT classmate billert stepped up as well to help manage the competition and arrange a partnership with another student-run STEM educational organization, Buzzonline (buzzonline.org). Together, we are the three OMMC directors and have worked tirelessly to bring this contest to fruition. We also cannot thank our fellow staff members enough for the work and effort they have put into this organization as well. As of now, we also provide a monthly resource via the Problem of the Month, as well as some Youtube content coming soon. You can find some of this on this AoPS thread: https:\/\/artofproblemsolving.com\/community\/c5h2731203<\/a>
\n
\nWhat happened in OMMC Year 1?
\n<\/b>
\nOMMC Year 1 was for the most part a big success! We had 230+ participants from around the world take part in the competition, and the winners came away with hundreds of dollars in prizes! Questions were high quality and the test went smoothly.
\n
\nIs this going to be exactly the same as OMMC Year 2?
\n<\/b>
\nChange is good! We\u2019re dramatically switching things up for OMMC Year 2. We\u2019re going to have one single team round with 25 questions, and teams can be up to 4 people.<\/b> The test is untimed<\/b>: you\u2019re going to have around a week to work on the problems with your team. Most importantly, the questions are just going to be better this time around.
\n
\nHow are the problems?
\n<\/b>
\nOnly the best problems by our panel of dedicated and talented problem writers have been selected. Hundreds of problems have been comprehensively reviewed by our panel of equally wonderful testsolvers. Our content creation staff has achieved pretty much every mathematical achievement possible! Staff members have qualified for AIME, excelled at USAMO and USAJMO, and attended MOP.<\/b> Our staff members have contributed to countless student-led math organizations and competitions<\/b> in the past and we all have a high degree of mathematical experience under our belt. I believe that OMMC Year 2 contains some of our best work yet.
\n
\nHere are sample problems that we encourage prospective contestants to try.
\n
\nhttps:\/\/artofproblemsolving.com\/community\/c2825027<\/a>
\n
\nOr, check out the problems from last year\u2019s contest:
\n
\nhttps:\/\/artofproblemsolving.com\/community\/c1976711<\/a>
\n
\nSome high quality mock contests that have been contributed to by OMMC Staff Members include SADGIME<\/a>, POGIME<\/a>, and AAMC<\/a>. Other contests staff members have contributed heavily to include ADMC<\/a> and OYMC<\/a>.
\n
\nHow hard is it?
\n<\/b>
\nWe have designed the test to be accessible to beginners at the early end but also challenging to experts on the late end. The early questions will be around the difficulty of easy questions from the AMC 10\/12. Later questions will be at or exceeding the difficulty of the hardest questions from the AIME. We hope that teams will collaborate and think deeply about the problems on the test.
\n
\nHow do we sign up?
\n<\/b>
\nYou won\u2019t have to! You\u2019ll just put in your information as you submit the test, since it\u2019s untimed. However, we do encourage you to \u201csign up\u201d on this thread, just like how you might with a mock contest. This isn\u2019t required to take the test nor does it force you to take the test. But it\u2019s a great way to show support for us and bump the thread to the top of the forums, so we do appreciate it!
\n
\nHow will the test be held?
\n<\/b>
\nWe highly recommend competitors join our Community Discord<\/b> for the latest updates on the competition, as well as for finding team members to team up with. However, all the important information will also be updated on this thread as necessary. Each team can consist of between 1 and 4 people, inclusive. Each competitor in a team has to be 18 or younger to be eligible for the competition.<\/b>
\n
\nSolo participants are allowed and will be treated simply as one man teams. They will be eligible for the same prizes as teams with multiple people.
\n
\nOur test will be held completely online and untimed. There will be one single test of 25 questions that all members of the team can access. Each question has a nonnegative integer answer. Each question is weighted equally, so each team will receive a single score out of 25.
\n
\nAs for what is allowed, we do not allow the use of anything other than writing utensils, scratch paper, compass, ruler\/straightedge, and a single four function calculator (addition, subtraction, multiplication, division). In particular, the use of websites such as Wolfram Alpha, Geogebra, Symbolab, and\/or Desmos is not allowed. Competitors can only communicate about the test with the people in their team. Collaboration between teams or between a team and an individual not on the team, is prohibited. If we find any violations of academic integrity, we will disqualify all teams involved.
\n
\nTiebreaker rounds will be given out if necessary after the contest period has ended. We will contact teams through email for this.
\n
\nOn May 27th, we\u2019ll put out a link by which teams can register and access the test. Teams will put in their registration information as they submit the test. For now, we recommend competitors to search for team members and join the OMMC Discord Community for further updates.
\n
\nPrizes?
\n<\/b>
\nPrizes shouldn\u2019t be the main reason someone takes OMMC, but in previous years we have been sponsored by organizations such as AoPS, Maplesoft, and Wolfram Alpha, who have provided hundreds of dollars to top scoring competitors.
\n
\nThis year, we have a 45 dollar Desmos Gift Card Code, 300 dollars in gift cards and T-shirts from Jane Street, a 500 dollar Geogebra Webinar, 100 dollars in AoPS coupons, and 3600 dollars in Wolfram Alpha Notebook Editions to give out so far. We are happy to announce that Maplesoft will be sponsoring us with $168 value in 4 Maple Learn Premium accounts, active for 6 months, that will be given to the winning team. More updates on prizes coming soon. <\/b>
\n
\nSome of these prizes will be raffled out! You just need to put in a submission to be eligible.<\/b> Spread the news and keep the signups going, you do NOT want to miss this opportunity!
\n
\nI have more questions. Who do I ask?
\n<\/b>
\nWe respond most quickly on our community discord, but you can also contact us through email via the ommcofficial@gmail.com address.
\n
\nWe hope for your participation, and good luck!
\n<\/b>
\nsquareman & the OMMC staff","post_canonical":"After a long wait we\u2019re back and better than ever!\n\n[size=200]Hello to all creative problem solvers,\n[\/size]\nDo you want to work on a fun, untimed team math competition with amazing questions?\n\nDo you want to have a chance (just by taking a test!) to win prizes?\n\nAfter more than a year and thousands of hours of hard work, the [hide=OMMC staff]squareman, billert, TempestGamer327, CatsAway, Penguin_Puddles, naman12, bissue, ike.chen, jacoporizzo, v4913, ApraTrip, bryanguo, nicksms, cj13609517288, vsamc, AP01, Kevnut_937, studentahere, vinay_0606, marmoset, Lemonberry, focus1111, DottedCalculator, sotpidot, JustinLee2017, rocketsri, bradygho, ritwin, RP3.1415, Serena_Xu, YBSuburbanTea[\/hide] would like to present to you the \n\n[size=200]Online Monmouth Math Competition!\n[\/size]\n\nUse the link [b][url]http:\/\/www.ommcofficial.org\/[\/url] or [url]https:\/\/ommc-website.vercel.app\/[\/url]. Check out our shiny new website with all the important information you need![\/b]\n\n[b]This is not a local competition; any student 18 or younger anywhere in the world can attend. We have changed some elements of our contest format, so read this announcement carefully and thoroughly! Our website is currently down but we will let you know when it gets back up. Thanks for your understanding![\/b]\n\nYou may have seen our [url=https:\/\/artofproblemsolving.com\/community\/c5h2731203]earlier hype announcement[\/url]. We will still be posting on that thread with Problem of the Months and new video releases. But this is where we will post all updates about the competition.\n\n[b]When is this? \n[\/b]\nThe test will be released on [b]May 27th and will be due on June 5th[\/b], tentatively (10 days to work on it). Mark your calendars!\n\n[b]Who runs this?\n[\/b]\nThe Online Monmouth Math Competition (OMMC) for short was founded by a school friend (TempestGamer327) as well as myself. Later, a fellow WOOT classmate billert stepped up as well to help manage the competition and arrange a partnership with another student-run STEM educational organization, Buzzonline (buzzonline.org). Together, we are the three OMMC directors and have worked tirelessly to bring this contest to fruition. We also cannot thank our fellow staff members enough for the work and effort they have put into this organization as well. As of now, we also provide a monthly resource via the Problem of the Month, as well as some Youtube content coming soon. You can find some of this on this AoPS thread: [url]https:\/\/artofproblemsolving.com\/community\/c5h2731203[\/url]\n\n[b]What happened in OMMC Year 1?\n[\/b]\nOMMC Year 1 was for the most part a big success! We had 230+ participants from around the world take part in the competition, and the winners came away with hundreds of dollars in prizes! Questions were high quality and the test went smoothly. \n\n[b]Is this going to be exactly the same as OMMC Year 2?\n[\/b]\nChange is good! We\u2019re dramatically switching things up for OMMC Year 2. We\u2019re going to have [b]one single team round with 25 questions, and teams can be up to 4 people.[\/b] The test is [b]untimed[\/b]: you\u2019re going to have around a week to work on the problems with your team. Most importantly, the questions are just going to be better this time around. \n\n[b]How are the problems?\n[\/b]\nOnly the best problems by our panel of dedicated and talented problem writers have been selected. Hundreds of problems have been comprehensively reviewed by our panel of equally wonderful testsolvers. Our content creation staff has achieved pretty much every mathematical achievement possible! Staff members have [b]qualified for AIME, excelled at USAMO and USAJMO, and attended MOP.[\/b] Our staff members have contributed to [b]countless student-led math organizations and competitions[\/b] in the past and we all have a high degree of mathematical experience under our belt. I believe that OMMC Year 2 contains some of our best work yet. \n\nHere are sample problems that we encourage prospective contestants to try.\n\n[url]https:\/\/artofproblemsolving.com\/community\/c2825027[\/url]\n\nOr, check out the problems from last year\u2019s contest: \n\n[url]https:\/\/artofproblemsolving.com\/community\/c1976711[\/url]\n\nSome high quality mock contests that have been contributed to by OMMC Staff Members include [url=https:\/\/artofproblemsolving.com\/community\/c594864t183f594864h2550289_sadgime__mock_aime_test_concluded]SADGIME[\/url], [url=https:\/\/artofproblemsolving.com\/community\/c594864t183f594864h2470832_pogime__mock_aime_released]POGIME[\/url], and [url=https:\/\/artofproblemsolving.com\/community\/c594864t183f594864h2690325_aaime_released_aamc_810aime_series]AAMC[\/url]. Other contests staff members have contributed heavily to include [url=https:\/\/artofproblemsolving.com\/community\/q1h2665919p23098559]ADMC[\/url] and [url=https:\/\/artofproblemsolving.com\/community\/q2h2535331p21573474]OYMC[\/url].\n\n[b]How hard is it?\n[\/b]\nWe have designed the test to be accessible to beginners at the early end but also challenging to experts on the late end. The early questions will be around the difficulty of easy questions from the AMC 10\/12. Later questions will be at or exceeding the difficulty of the hardest questions from the AIME. We hope that teams will collaborate and think deeply about the problems on the test.\n\n[b]How do we sign up?\n[\/b]\nYou won\u2019t have to! You\u2019ll just put in your information as you submit the test, since it\u2019s untimed. However, we do encourage you to \u201csign up\u201d on this thread, just like how you might with a mock contest. This isn\u2019t required to take the test nor does it force you to take the test. But it\u2019s a great way to show support for us and bump the thread to the top of the forums, so we do appreciate it!\n\n[b]How will the test be held?\n[\/b]\nWe highly recommend competitors join our [b]Community Discord[\/b] for the latest updates on the competition, as well as for finding team members to team up with. However, all the important information will also be updated on this thread as necessary. [b]Each team can consist of between 1 and 4 people, inclusive. Each competitor in a team has to be 18 or younger to be eligible for the competition.[\/b]\n\nSolo participants are allowed and will be treated simply as one man teams. They will be eligible for the same prizes as teams with multiple people. \n\nOur test will be held completely online and untimed. There will be one single test of 25 questions that all members of the team can access. Each question has a nonnegative integer answer. Each question is weighted equally, so each team will receive a single score out of 25. \n\nAs for what is allowed, we do not allow the use of anything other than writing utensils, scratch paper, compass, ruler\/straightedge, and a single four function calculator (addition, subtraction, multiplication, division). In particular, the use of websites such as Wolfram Alpha, Geogebra, Symbolab, and\/or Desmos is not allowed. Competitors can only communicate about the test with the people in their team. Collaboration between teams or between a team and an individual not on the team, is prohibited. If we find any violations of academic integrity, we will disqualify all teams involved. \n\nTiebreaker rounds will be given out if necessary after the contest period has ended. We will contact teams through email for this. \n\nOn May 27th, we\u2019ll put out a link by which teams can register and access the test. Teams will put in their registration information as they submit the test. For now, we recommend competitors to search for team members and join the OMMC Discord Community for further updates. \n\n[b]Prizes?\n[\/b]\nPrizes shouldn\u2019t be the main reason someone takes OMMC, but in previous years we have been sponsored by organizations such as AoPS, Maplesoft, and Wolfram Alpha, who have provided hundreds of dollars to top scoring competitors. \n\n[b]This year, we have a 45 dollar Desmos Gift Card Code, 300 dollars in gift cards and T-shirts from Jane Street, a 500 dollar Geogebra Webinar, 100 dollars in AoPS coupons, and 3600 dollars in Wolfram Alpha Notebook Editions to give out so far. We are happy to announce that Maplesoft will be sponsoring us with $168 value in 4 Maple Learn Premium accounts, active for 6 months, that will be given to the winning team. More updates on prizes coming soon. [\/b]\n\n[b]Some of these prizes will be raffled out! You just need to put in a submission to be eligible.[\/b] Spread the news and keep the signups going, you do NOT want to miss this opportunity!\n\n[b]I have more questions. Who do I ask?\n[\/b]\nWe respond most quickly on our community discord, but you can also contact us through email via the ommcofficial@gmail.com address.\n\n[b]We hope for your participation, and good luck! \n[\/b]\nsquareman & the OMMC staff","username":"squareman","reported":false,"is_thanked":false,"is_nothanked":false,"attachment":false,"thanks_received":57,"nothanks_received":0,"thankers":"pog, RP3.1415, teasaffrontaffy, Bole, StopSine, Mogmog8, rayfish, Jndd, Bradygho, mahaler, mathleticguyyy, v4913, bissue, JustinLee2017, LemonBerry, rosegold248, vsamc, megarnie, Math4Life2020, ApraTrip, Robomania_534, Catsaway, HamstPan38825, studentahere, AlphaBetaGammaOmega, YBSuburbanTea, bryanguo, cj13609517288, jacoporizzo, CT17, andiesmountain, CyclicISLscelesTrapezoid, rocketsri, TempestGamer237, awesomehuman, rama1728, Ninjasolver0201, megahertz13, ImSh95, son7, Focus1111, ostriches88, billert, skyguy88, russellk, Sross314, GoodMorning, Lamboreghini, Jc426, justJen, centslordm, PlayfulOwl-aops, IMOTC, GoldenOstraprey, crazyeyemoody907, rg_ryse, wxl18","deleted":false,"post_number":1,"post_time":1651623059,"num_edits":17,"post_format":"bbcode","last_edit_time":1652916491,"last_editor_username":"squareman","last_edit_reason":"","admin":false,"avatar":"\/\/avatar.artofproblemsolving.com\/avatar_311064.jpeg?t=1612816163","num_posts":666,"editable":false,"deletable":false,"show_from_start":true,"show_from_end":false}],"topic_id":2837951,"comment_count":113,"num_deleted":8,"topic_title":"[Confirmed $4713+ in Prizes And Counting] OMMC Contest 2022: Back For Year 2!","target_url":"","target_text":"","topic_type":"forum","state":"none","first_post_id":25130022,"first_poster_id":311064,"first_post_time":1651623059,"first_poster_name":"squareman","last_post_time":1653060186,"first_poster_avatar":"\/\/avatar.artofproblemsolving.com\/avatar_311064.jpeg?t=1612816163","last_poster_avatar":"\/\/avatar.artofproblemsolving.com\/avatar_621129.png","last_post_id":25249397,"last_poster_id":621129,"last_poster_name":"fuzimiao2013","last_update_time":1653060186,"category_id":5,"is_public":true,"roles":{"53544":"mod","93494":"mod","86424":"mod","1662":"mod","38516":"mod","242520":"mod","159507":"mod","565384":"mod"},"tags":[{"tag_id":1142827,"tag_text":"ommc","is_visible":true},{"tag_id":30818,"tag_text":"math competition","is_visible":true},{"tag_id":63310,"tag_text":"High school math","is_visible":true},{"tag_id":31581,"tag_text":"Math Competitions","is_visible":true}],"can_have_source":true,"locked":false,"forum_locked":0,"announce_type":"none","announce_through":"","announce_factor":0,"preview":"After a long wait we\u2019re back and better than ever!
\n
\nHello to all creative problem solvers,
\n
\nDo you want to work on a fun, untimed team math competition with amazing questions?
\n
\nDo you want to have a chance (just by taking a test!) to win prizes?
\n
\nAfter more than a year and thousands of hours of hard work, the OMMC staff<\/span>
squareman, billert, TempestGamer327, CatsAway, Penguin_Puddles, naman12, bissue, ike.chen, jacoporizzo, v4913, ApraTrip, bryanguo, nicksms, cj13609517288, vsamc, AP01, Kevnut_937, studentahere, vinay_0606, marmoset, Lemonberry, focus1111, DottedCalculator, sotpidot, JustinLee2017, rocketsri, bradygho, ritwin, RP3.1415, Serena_Xu, YBSuburbanTea<\/div> would like to present to you the
\n
\nOnline Monmouth Math Competition!
\n
\n
\nUse the link http:\/\/www.ommcofficial.org\/<\/a> or https:\/\/ommc-website.vercel.app\/<\/a>. Check out our shiny new website with all the important information you need!<\/b>
\n
\nThis is not a local competition; any student 18 or younger anywhere in the world can attend. We have changed some elements of our contest format, so read this announcement carefully and thoroughly! Our website is currently down but we will let you know when it gets back up. Thanks for your understanding!<\/b>
\n
\nYou may have seen our earlier hype announcement<\/a>. We will still be posting on that thread with Problem of the Months and new video releases. But this is where we will post all updates about the competition.
\n
\nWhen is this?
\n<\/b>
\nThe test will be released on May 27th and will be due on June 5th<\/b>, tentatively (10 days to work on it). Mark your calendars!
\n
\nWho runs this?
\n<\/b>
\nThe Online Monmouth Math Competition (OMMC) for short was founded by a school friend (TempestGamer327) as well as myself. Later, a fellow WOOT classmate billert stepped up as well to help manage the competition and arrange a partnership with another student-run STEM educational organization, Buzzonline (buzzonline.org). Together, we are the three OMMC directors and have worked tirelessly to bring this contest to fruition. We also cannot thank our fellow staff members enough for the work and effort they have put into this organization as well. As of now, we also provide a monthly resource via the Problem of the Month, as well as some Youtube content coming soon. You can find some of this on this AoPS thread: https:\/\/artofproblemsolving.com\/community\/c5h2731203<\/a>
\n
\nWhat happened in OMMC Year 1?
\n<\/b>
\nOMMC Year 1 was for the most part a big success! We had 230+ participants from around the world take part in the competition, and the winners came away with hundreds of dollars in prizes! Questions were high quality and the test went smoothly.
\n
\nIs this going to be exactly the same as OMMC Year 2?
\n<\/b>
\nChange is good! We\u2019re dramatically switching things up for OMMC Year 2. We\u2019re going to have one single team round with 25 questions, and teams can be up to 4 people.<\/b> The test is untimed<\/b>: you\u2019re going to have around a week to work on the problems with your team. Most importantly, the questions are just going to be better this time around.
\n
\nHow are the problems?
\n<\/b>
\nOnly the best problems by our panel of dedicated and talented problem writers have been selected. Hundreds of problems have been comprehensively reviewed by our panel of equally wonderful testsolvers. Our content creation staff has achieved pretty much every mathematical achievement possible! Staff members have qualified for AIME, excelled at USAMO and USAJMO, and attended MOP.<\/b> Our staff members have contributed to countless student-led math organizations and competitions<\/b> in the past and we all have a high degree of mathematical experience under our belt. I believe that OMMC Year 2 contains some of our best work yet.
\n
\nHere are sample problems that we encourage prospective contestants to try.
\n
\nhttps:\/\/artofproblemsolving.com\/community\/c2825027<\/a>
\n
\nOr, check out the problems from last year\u2019s contest:
\n
\nhttps:\/\/artofproblemsolving.com\/community\/c1976711<\/a>
\n
\nSome high quality mock contests that have been contributed to by OMMC Staff Members include SADGIME<\/a>, POGIME<\/a>, and AAMC<\/a>. Other contests staff members have contributed heavily to include ADMC<\/a> and OYMC<\/a>.
\n
\nHow hard is it?
\n<\/b>
\nWe have designed the test to be accessible to beginners at the early end but also challenging to experts on the late end. The early questions will be around the difficulty of easy questions from the AMC 10\/12. Later questions will be at or exceeding the difficulty of the hardest questions from the AIME. We hope that teams will collaborate and think deeply about the problems on the test.
\n
\nHow do we sign up?
\n<\/b>
\nYou won\u2019t have to! You\u2019ll just put in your information as you submit the test, since it\u2019s untimed. However, we do encourage you to \u201csign up\u201d on this thread, just like how you might with a mock contest. This isn\u2019t required to take the test nor does it force you to take the test. But it\u2019s a great way to show support for us and bump the thread to the top of the forums, so we do appreciate it!
\n
\nHow will the test be held?
\n<\/b>
\nWe highly recommend competitors join our Community Discord<\/b> for the latest updates on the competition, as well as for finding team members to team up with. However, all the important information will also be updated on this thread as necessary. Each team can consist of between 1 and 4 people, inclusive. Each competitor in a team has to be 18 or younger to be eligible for the competition.<\/b>
\n
\nSolo participants are allowed and will be treated simply as one man teams. They will be eligible for the same prizes as teams with multiple people.
\n
\nOur test will be held completely online and untimed. There will be one single test of 25 questions that all members of the team can access. Each question has a nonnegative integer answer. Each question is weighted equally, so each team will receive a single score out of 25.
\n
\nAs for what is allowed, we do not allow the use of anything other than writing utensils, scratch paper, compass, ruler\/straightedge, and a single four function calculator (addition, subtraction, multiplication, division). In particular, the use of websites such as Wolfram Alpha, Geogebra, Symbolab, and\/or Desmos is not allowed. Competitors can only communicate about the test with the people in their team. Collaboration between teams or between a team and an individual not on the team, is prohibited. If we find any violations of academic integrity, we will disqualify all teams involved.
\n
\nTiebreaker rounds will be given out if necessary after the contest period has ended. We will contact teams through email for this.
\n
\nOn May 27th, we\u2019ll put out a link by which teams can register and access the test. Teams will put in their registration information as they submit the test. For now, we recommend competitors to search for team members and join the OMMC Discord Community for further updates.
\n
\nPrizes?
\n<\/b>
\nPrizes shouldn\u2019t be the main reason someone takes OMMC, but in previous years we have been sponsored by organizations such as AoPS, Maplesoft, and Wolfram Alpha, who have provided hundreds of dollars to top scoring competitors.
\n
\nThis year, we have a 45 dollar Desmos Gift Card Code, 300 dollars in gift cards and T-shirts from Jane Street, a 500 dollar Geogebra Webinar, 100 dollars in AoPS coupons, and 3600 dollars in Wolfram Alpha Notebook Editions to give out so far. We are happy to announce that Maplesoft will be sponsoring us with $168 value in 4 Maple Learn Premium accounts, active for 6 months, that will be given to the winning team. More updates on prizes coming soon. <\/b>
\n
\nSome of these prizes will be raffled out! You just need to put in a submission to be eligible.<\/b> Spread the news and keep the signups going, you do NOT want to miss this opportunity!
\n
\nI have more questions. Who do I ask?
\n<\/b>
\nWe respond most quickly on our community discord, but you can also contact us through email via the ommcofficial@gmail.com address.
\n
\nWe hope for your participation, and good luck!
\n<\/b>
\nsquareman & the OMMC staff","category_name":"Contests & Programs","category_main_color":"#008fd5","category_secondary_color":"#d9effd","num_reports":0,"poll_id":0,"source":"OMMC Year 2","category_num_users":7,"category_num_topics":29049,"category_num_posts":471543,"num_views":7032,"cat_can_target":0,"has_thanks":true,"has_nothanks":false,"is_bookmarked":false,"in_feed":false,"is_watched":false},"2848452":{"num_posts":8,"posts_data":[{"post_id":25246825,"topic_id":2848452,"poster_id":883645,"post_rendered":"I was wondering what are some good competitions to do over the summer.","post_canonical":"I was wondering what are some good competitions to do over the summer.","username":"bjump","reported":false,"is_thanked":false,"is_nothanked":false,"attachment":false,"thanks_received":0,"nothanks_received":0,"thankers":null,"deleted":false,"post_number":1,"post_time":1653009052,"num_edits":0,"post_format":"bbcode","last_edit_time":0,"last_editor_username":"","last_edit_reason":"","admin":false,"avatar":"\/\/avatar.artofproblemsolving.com\/avatar_883645.jpg?t=1650582876","num_posts":57,"editable":false,"deletable":false,"show_from_start":true,"show_from_end":false}],"topic_id":2848452,"comment_count":8,"num_deleted":0,"topic_title":"Summer math competitions","target_url":"","target_text":"","topic_type":"forum","state":"none","first_post_id":25246825,"first_poster_id":883645,"first_post_time":1653009052,"first_poster_name":"bjump","last_post_time":1653057830,"first_poster_avatar":"\/\/avatar.artofproblemsolving.com\/avatar_883645.jpg?t=1650582876","last_poster_avatar":"\/\/avatar.artofproblemsolving.com\/avatar_514183.png?t=1630367279","last_post_id":25249216,"last_poster_id":514183,"last_poster_name":"bobthegod78","last_update_time":1653057830,"category_id":5,"is_public":true,"roles":{"53544":"mod","93494":"mod","86424":"mod","1662":"mod","38516":"mod","242520":"mod","159507":"mod","565384":"mod"},"tags":[{"tag_id":29415,"tag_text":"summer programs","is_visible":true}],"can_have_source":true,"locked":false,"forum_locked":0,"announce_type":"none","announce_through":"","announce_factor":0,"preview":"I was wondering what are some good competitions to do over the summer.","category_name":"Contests & Programs","category_main_color":"#008fd5","category_secondary_color":"#d9effd","num_reports":0,"poll_id":0,"source":"","category_num_users":7,"category_num_topics":29049,"category_num_posts":471543,"num_views":361,"cat_can_target":0,"has_thanks":true,"has_nothanks":false,"is_bookmarked":false,"in_feed":false,"is_watched":false}};AoPS.preload_topics[6]={"2835390":{"num_posts":10,"posts_data":[{"post_id":25099531,"topic_id":2835390,"poster_id":621197,"post_rendered":"Let be a convex quadrilateral, the incenters of ![\"$\\triangle](\"\/\/latex.artofproblemsolving.com\/8\/c\/3\/8c3a2d2224f7d163b46d702132425d47828bf538.png\")
and ![\"$\\triangle](\"\/\/latex.artofproblemsolving.com\/b\/8\/e\/b8eabc87afe4c11a47e4aa27628d5517af4866b9.png\")
are ![\"$I,J$\"](\"\/\/latex.artofproblemsolving.com\/b\/0\/a\/b0a151a192d1846a8561e6dd87f893af7efbb262.png\")
,<\/span> respectively. It is known that ![\"$AC,BD,IJ$\"](\"\/\/latex.artofproblemsolving.com\/8\/4\/d\/84d67e0f07ea443c3a18b8221c7f55d31f810b0e.png\")
concurrent at a point ![\"$P$\"](\"\/\/latex.artofproblemsolving.com\/4\/b\/4\/4b4cade9ca8a2c8311fafcf040bc5b15ca507f52.png\")
.<\/span> The line perpendicular to through intersects with the outer angle bisector of ![\"$\\angle](\"\/\/latex.artofproblemsolving.com\/c\/b\/5\/cb55dc9c50a80e1d9eb23fe53e45f464c0ac755e.png\")
and the outer angle bisector ![\"$\\angle](\"\/\/latex.artofproblemsolving.com\/2\/3\/3\/23386faeefe37629243fa264877b288499db5048.png\")
at ![\"$E,F$\"](\"\/\/latex.artofproblemsolving.com\/2\/5\/0\/250f765e0f0b3842f9d095dc0a3569905d344ce8.png\")
,<\/span> respectively. Show that ![\"$PE=PF$\"](\"\/\/latex.artofproblemsolving.com\/e\/e\/f\/eef01363603050cadb084777489b45552600fa2b.png\")
.<\/span>","post_canonical":"Let $ABCD$ be a convex quadrilateral, the incenters of $\\triangle ABC$ and $\\triangle ADC$ are $I,J$, respectively. It is known that $AC,BD,IJ$ concurrent at a point $P$. The line perpendicular to $BD$ through $P$ intersects with the outer angle bisector of $\\angle BAD$ and the outer angle bisector $\\angle BCD$ at $E,F$, respectively. Show that $PE=PF$.","username":"JustPostChinaTST","reported":false,"is_thanked":false,"is_nothanked":false,"attachment":false,"thanks_received":1,"nothanks_received":0,"thankers":"ImSh95","deleted":false,"post_number":1,"post_time":1651333706,"num_edits":3,"post_format":"bbcode","last_edit_time":1651507883,"last_editor_username":"JustPostChinaTST","last_edit_reason":"typos","admin":false,"avatar":"\/\/avatar.artofproblemsolving.com\/avatar_621197.png","num_posts":38,"editable":false,"deletable":false,"show_from_start":true,"show_from_end":false}],"topic_id":2835390,"comment_count":10,"num_deleted":0,"topic_title":"Concurrency in a quadrilateral implies equal length","target_url":"","target_text":"","topic_type":"forum","state":"none","first_post_id":25099531,"first_poster_id":621197,"first_post_time":1651333706,"first_poster_name":"JustPostChinaTST","last_post_time":1653072112,"first_poster_avatar":"\/\/avatar.artofproblemsolving.com\/avatar_621197.png","last_poster_avatar":"\/\/avatar.artofproblemsolving.com\/avatar_682170.png","last_post_id":25250488,"last_poster_id":682170,"last_poster_name":"hakN","last_update_time":1653072112,"category_id":6,"is_public":true,"roles":{"2":"mod","432":"mod","38516":"mod","53544":"mod","285":"mod","93494":"mod","67223":"mod","56597":"mod","242520":"mod","159507":"mod"},"tags":[{"tag_id":48,"tag_text":"geometry","is_visible":true},{"tag_id":120,"tag_text":"incenter","is_visible":true},{"tag_id":124,"tag_text":"angle bisector","is_visible":true}],"can_have_source":true,"locked":false,"forum_locked":0,"announce_type":"none","announce_through":"","announce_factor":0,"preview":"Let be a convex quadrilateral, the incenters of and are ,<\/span> respectively. It is known that concurrent at a point .<\/span> The line perpendicular to through intersects with the outer angle bisector of and the outer angle bisector at ,<\/span> respectively. Show that .<\/span>","category_name":"High School Olympiads","category_main_color":"#029386","category_secondary_color":"#e1fff2","num_reports":0,"poll_id":0,"source":"2022 China TST, Test 4 P2","category_num_users":28,"category_num_topics":275645,"category_num_posts":1201306,"num_views":1160,"cat_can_target":0,"has_thanks":true,"has_nothanks":false,"is_bookmarked":false,"in_feed":false,"is_watched":false},"1374313":{"num_posts":7,"posts_data":[{"post_id":7587802,"topic_id":1374313,"poster_id":232609,"post_rendered":"Let be a cyclic quadrilateral. The diagonals and meet at ,<\/span> and ![\"$DA](\"\/\/latex.artofproblemsolving.com\/c\/0\/2\/c021ecae123b8c58ceff108d560db0544f0ccb8e.png\")
and ![\"$CB$\"](\"\/\/latex.artofproblemsolving.com\/3\/e\/3\/3e3a4ec0df571e719bd3f1d7e00bf71fc55ba2b9.png\")
meet at ![\"$Q$\"](\"\/\/latex.artofproblemsolving.com\/9\/8\/6\/9866e3a998d628ba0941eb4fea0666ac391d149a.png\")
.<\/span> Suppose ![\"$PQ$\"](\"\/\/latex.artofproblemsolving.com\/7\/a\/b\/7ab17967324fc2b12349c0610c6c256f4c829162.png\")
is perpendicular to .<\/span> Let be the midpoint of .<\/span> Prove that ![\"$PE$\"](\"\/\/latex.artofproblemsolving.com\/0\/e\/d\/0edebe902653b343eee6f0a6a93a09f80884504e.png\")
is perpendicular to .<\/span>","post_canonical":"Let $ABCD$ be a cyclic quadrilateral. The diagonals $AC$ and $BD$ meet at $P$, and $DA $ and $CB$ meet at $Q$. Suppose $PQ$ is perpendicular to $AC$. Let $E$ be the midpoint of $AB$. Prove that $PE$ is perpendicular to $BC$.","username":"sualehasif996","reported":false,"is_thanked":false,"is_nothanked":false,"attachment":false,"thanks_received":0,"nothanks_received":0,"thankers":null,"deleted":false,"post_number":1,"post_time":1485630962,"num_edits":2,"post_format":"bbcode","last_edit_time":1485631009,"last_editor_username":"sualehasif996","last_edit_reason":"","admin":false,"avatar":"\/\/avatar.artofproblemsolving.com\/avatar_232609.png","num_posts":110,"editable":false,"deletable":false,"show_from_start":true,"show_from_end":false}],"topic_id":1374313,"comment_count":7,"num_deleted":0,"topic_title":"Perpendicularity in Cyclic Quad.","target_url":"","target_text":"","topic_type":"forum","state":"none","first_post_id":7587802,"first_poster_id":232609,"first_post_time":1485630962,"first_poster_name":"sualehasif996","last_post_time":1653071847,"first_poster_avatar":"\/\/avatar.artofproblemsolving.com\/avatar_232609.png","last_poster_avatar":"\/\/avatar.artofproblemsolving.com\/avatar_421983.png?t=1559877586","last_post_id":25250472,"last_poster_id":421983,"last_poster_name":"TheCoolDinosuar","last_update_time":1653071847,"category_id":6,"is_public":true,"roles":{"2":"mod","432":"mod","38516":"mod","53544":"mod","285":"mod","93494":"mod","67223":"mod","56597":"mod","242520":"mod","159507":"mod"},"tags":[{"tag_id":210,"tag_text":"cyclic quadrilateral","is_visible":true},{"tag_id":129996,"tag_text":"perpendicular lines","is_visible":true},{"tag_id":48,"tag_text":"geometry","is_visible":true}],"can_have_source":true,"locked":false,"forum_locked":0,"announce_type":"none","announce_through":"","announce_factor":0,"preview":"Let be a cyclic quadrilateral. The diagonals and meet at ,<\/span> and and meet at .<\/span> Suppose is perpendicular to .<\/span> Let be the midpoint of .<\/span> Prove that is perpendicular to .<\/span>","category_name":"High School Olympiads","category_main_color":"#029386","category_secondary_color":"#e1fff2","num_reports":0,"poll_id":0,"source":"Pakistan TST(2) 2017.P1","category_num_users":28,"category_num_topics":275645,"category_num_posts":1201306,"num_views":1948,"cat_can_target":0,"has_thanks":true,"has_nothanks":false,"is_bookmarked":false,"in_feed":false,"is_watched":false},"1859980":{"num_posts":6,"posts_data":[{"post_id":12577384,"topic_id":1859980,"poster_id":212018,"post_rendered":"Show that for each non-negative integer ![\"$n$\"](\"\/\/latex.artofproblemsolving.com\/1\/7\/4\/174fadd07fd54c9afe288e96558c92e0c1da733a.png\")
there are unique non-negative integers ![\"$x$\"](\"\/\/latex.artofproblemsolving.com\/2\/6\/e\/26eeb5258ca5099acf8fe96b2a1049c48c89a5e6.png\")
and ![\"$y$\"](\"\/\/latex.artofproblemsolving.com\/0\/9\/2\/092e364e1d9d19ad5fffb0b46ef4cc7f2da02c1c.png\")
such that we have
\n![\"\\[n=\\frac{(x+y)^2+3x+y}{2}.\\]\"](\"\/\/latex.artofproblemsolving.com\/2\/3\/d\/23d613de9144302e447e689290b06e3228b70dd3.png\")
","post_canonical":"Show that for each non-negative integer $n$ there are unique non-negative integers $x$ and $y$ such that we have\n\\[n=\\frac{(x+y)^2+3x+y}{2}.\\]","username":"Tintarn","reported":false,"is_thanked":false,"is_nothanked":false,"attachment":false,"thanks_received":1,"nothanks_received":0,"thankers":"ImSh95","deleted":false,"post_number":1,"post_time":1561022834,"num_edits":0,"post_format":"bbcode","last_edit_time":0,"last_editor_username":"","last_edit_reason":"","admin":false,"avatar":"\/\/avatar.artofproblemsolving.com\/avatar_212018.png","num_posts":7691,"editable":false,"deletable":false,"show_from_start":true,"show_from_end":false}],"topic_id":1859980,"comment_count":6,"num_deleted":0,"topic_title":"An old polynomial bijection between N and NxN","target_url":"","target_text":"","topic_type":"forum","state":"none","first_post_id":12577384,"first_poster_id":212018,"first_post_time":1561022834,"first_poster_name":"Tintarn","last_post_time":1653070495,"first_poster_avatar":"\/\/avatar.artofproblemsolving.com\/avatar_212018.png","last_poster_avatar":"\/\/avatar.artofproblemsolving.com\/avatar_693742.png","last_post_id":25250366,"last_poster_id":693742,"last_poster_name":"Joel.Gerlach","last_update_time":1653070495,"category_id":6,"is_public":true,"roles":{"2":"mod","432":"mod","38516":"mod","53544":"mod","285":"mod","93494":"mod","67223":"mod","56597":"mod","242520":"mod","159507":"mod"},"tags":[{"tag_id":169,"tag_text":"algebra","is_visible":true},{"tag_id":170,"tag_text":"polynomial","is_visible":true},{"tag_id":177,"tag_text":"number theory","is_visible":true}],"can_have_source":true,"locked":false,"forum_locked":0,"announce_type":"none","announce_through":"","announce_factor":0,"preview":"Show that for each non-negative integer there are unique non-negative integers and such that we have
\n","category_name":"High School Olympiads","category_main_color":"#029386","category_secondary_color":"#e1fff2","num_reports":0,"poll_id":0,"source":"Germany 2019, Problem 4","category_num_users":28,"category_num_topics":275645,"category_num_posts":1201306,"num_views":878,"cat_can_target":0,"has_thanks":true,"has_nothanks":false,"is_bookmarked":false,"in_feed":false,"is_watched":false},"2846808":{"num_posts":28,"posts_data":[{"post_id":25228662,"topic_id":2846808,"poster_id":786361,"post_rendered":"Let ![\"$a,b,c,d$\"](\"\/\/latex.artofproblemsolving.com\/b\/b\/6\/bb60e0857a2c0a2c47acfbe81781032feb1f7150.png\")
be real numbers such that ![\"$a^2+b^2+c^2+d^2=1$\"](\"\/\/latex.artofproblemsolving.com\/6\/6\/2\/6626ab951c68d4bdae445a5b6b3b99c7292c363d.png\")
.<\/span> Determine the minimum value of ![\"$(a-b)(b-c)(c-d)(d-a)$\"](\"\/\/latex.artofproblemsolving.com\/f\/e\/e\/fee4d3bbe65be2564ecad727d3973d78d81d159e.png\")
and determine all values of ![\"$(a,b,c,d)$\"](\"\/\/latex.artofproblemsolving.com\/f\/a\/e\/faedb9d30dc3763d92cbcacf2cc17e2bf64f3e8b.png\")
such that the minimum value is achived.","post_canonical":"Let $a,b,c,d$ be real numbers such that $a^2+b^2+c^2+d^2=1$. Determine the minimum value of $(a-b)(b-c)(c-d)(d-a)$ and determine all values of $(a,b,c,d)$ such that the minimum value is achived.","username":"Jalil_Huseynov","reported":false,"is_thanked":false,"is_nothanked":false,"attachment":false,"thanks_received":1,"nothanks_received":0,"thankers":"ImSh95","deleted":false,"post_number":1,"post_time":1652813445,"num_edits":0,"post_format":"bbcode","last_edit_time":0,"last_editor_username":"","last_edit_reason":"","admin":false,"avatar":"\/\/avatar.artofproblemsolving.com\/avatar_786361.png?t=1623049918","num_posts":377,"editable":false,"deletable":false,"show_from_start":true,"show_from_end":false}],"topic_id":2846808,"comment_count":28,"num_deleted":1,"topic_title":"Inequality on APMO P5","target_url":"","target_text":"","topic_type":"forum","state":"none","first_post_id":25228662,"first_poster_id":786361,"first_post_time":1652813445,"first_poster_name":"Jalil_Huseynov","last_post_time":1653070283,"first_poster_avatar":"\/\/avatar.artofproblemsolving.com\/avatar_786361.png?t=1623049918","last_poster_avatar":"\/\/avatar.artofproblemsolving.com\/avatar_202394.jpg?t=1595273230","last_post_id":25250347,"last_poster_id":202394,"last_poster_name":"Zezohabibullah","last_update_time":1653070283,"category_id":6,"is_public":true,"roles":{"2":"mod","432":"mod","38516":"mod","53544":"mod","285":"mod","93494":"mod","67223":"mod","56597":"mod","242520":"mod","159507":"mod"},"tags":[{"tag_id":243,"tag_text":"inequalities","is_visible":true},{"tag_id":30028,"tag_text":"APMO","is_visible":true},{"tag_id":1533779,"tag_text":"APMO 2022","is_visible":true}],"can_have_source":true,"locked":false,"forum_locked":0,"announce_type":"none","announce_through":"","announce_factor":0,"preview":"Let be real numbers such that .<\/span> Determine the minimum value of and determine all values of such that the minimum value is achived.","category_name":"High School Olympiads","category_main_color":"#029386","category_secondary_color":"#e1fff2","num_reports":0,"poll_id":0,"source":"APMO 2022 P5","category_num_users":28,"category_num_topics":275645,"category_num_posts":1201306,"num_views":2013,"cat_can_target":0,"has_thanks":true,"has_nothanks":false,"is_bookmarked":false,"in_feed":false,"is_watched":false}};AoPS.preload_topics[7]={"2847484":{"num_posts":2,"posts_data":[{"post_id":25236311,"topic_id":2847484,"poster_id":407889,"post_rendered":"Given u<\/b> = ![\"$(u,](\"\/\/latex.artofproblemsolving.com\/e\/4\/1\/e4162d79742879fcd196374e6e48a3f896087872.png\")
with ![\"$u=](\"\/\/latex.artofproblemsolving.com\/5\/4\/a\/54a27443b8529381ce18428ff378affaf9af3813.png\")
and ![\"$v=](\"\/\/latex.artofproblemsolving.com\/c\/9\/8\/c985a4b0346e01be6f9a06e95acbfdbc75a55fed.png\")
and the circle with radius ![\"$r](\"\/\/latex.artofproblemsolving.com\/0\/b\/d\/0bde359170829f653d087534939847c27a92cd2a.png\")
and center at the origin.
\n
\nEvaluate the integral of u<\/b>. dr<\/b>![\"$](\"\/\/latex.artofproblemsolving.com\/e\/1\/3\/e13ab851ecd5e9bfd436e89a608fdacd3cf2a846.png\")
![\"$dx$\"](\"\/\/latex.artofproblemsolving.com\/9\/5\/3\/953640113c8002037caa26af92570f9cb7d5773c.png\")
+ ![\"$v$\"](\"\/\/latex.artofproblemsolving.com\/a\/9\/f\/a9f23bf124b6b2b2a993eb313c72e678664ac74a.png\")
![\"$dy$\"](\"\/\/latex.artofproblemsolving.com\/5\/a\/6\/5a687ff25b068f70b5def1fdb4f1c49344997391.png\")
on the circle from the point ![\"$A](\"\/\/latex.artofproblemsolving.com\/7\/8\/6\/786c4ed8fdce54fb548034a4ff329c3c7dc0b8b4.png\")
to the point ![\"$B:](\"\/\/latex.artofproblemsolving.com\/d\/6\/c\/d6c84e1264b804b33f9a4e3b7fb8db0bbb58f29b.png\")
","post_canonical":"Given [b]u[\/b] = $(u, v)$ with $u= (e^x + 3x^2y)$ and $v= (e^{-y} + x^3 -4y^3)$ and the circle $C$ with radius $r = 1$ and center at the origin.\n\nEvaluate the integral of [b]u[\/b]. d[b]r[\/b] $ = u$ $dx$ + $v$ $dy$ on the circle from the point $A : (1, 0)$ to the point $B: (0, 1).$","username":"DurdonTyler","reported":false,"is_thanked":false,"is_nothanked":false,"attachment":false,"thanks_received":0,"nothanks_received":0,"thankers":null,"deleted":false,"post_number":1,"post_time":1652898282,"num_edits":0,"post_format":"bbcode","last_edit_time":0,"last_editor_username":"","last_edit_reason":"","admin":false,"avatar":"\/\/avatar.artofproblemsolving.com\/avatar_407889.png","num_posts":93,"editable":false,"deletable":true,"show_from_start":true,"show_from_end":false}],"topic_id":2847484,"comment_count":2,"num_deleted":0,"topic_title":"evaluate int on the circle from a to b","target_url":"","target_text":"","topic_type":"forum","state":"none","first_post_id":25236311,"first_poster_id":407889,"first_post_time":1652898282,"first_poster_name":"DurdonTyler","last_post_time":1653071393,"first_poster_avatar":"\/\/avatar.artofproblemsolving.com\/avatar_407889.png","last_poster_avatar":"\/\/avatar.artofproblemsolving.com\/avatar_407889.png","last_post_id":25250440,"last_poster_id":407889,"last_poster_name":"DurdonTyler","last_update_time":1653071393,"category_id":7,"is_public":true,"roles":{"432":"mod","93494":"mod","67223":"mod","9049":"mod","242520":"mod"},"tags":[{"tag_id":116,"tag_text":"calculus","is_visible":true}],"can_have_source":true,"locked":false,"forum_locked":0,"announce_type":"none","announce_through":"","announce_factor":0,"preview":"Given u<\/b> = with and and the circle with radius and center at the origin.
\n
\nEvaluate the integral of u<\/b>. dr<\/b> + on the circle from the point to the point ","category_name":"College Math","category_main_color":"#511e8f","category_secondary_color":"#f2e6fe","num_reports":0,"poll_id":0,"source":"","category_num_users":5,"category_num_topics":102698,"category_num_posts":402685,"num_views":51,"cat_can_target":0,"has_thanks":true,"has_nothanks":false,"is_bookmarked":false,"in_feed":false,"is_watched":false},"2846853":{"num_posts":2,"posts_data":[{"post_id":25229502,"topic_id":2846853,"poster_id":355854,"post_rendered":"Show that the power series for the function
\n![\"$$e^{ax}](\"\/\/latex.artofproblemsolving.com\/d\/8\/1\/d81856a3a61e5784dcfe52d905697a1a349edada.png\")
where ![\"$a,b](\"\/\/latex.artofproblemsolving.com\/b\/f\/8\/bf8da8bc169153bc137eb64cefeafc6283c91cbb.png\")
,<\/span> has either no zero coefficients or infinitely many zero coefficients.","post_canonical":"Show that the power series for the function\n$$e^{ax} \\cos bx,$$\nwhere $a,b >0$, has either no zero coefficients or infinitely many zero coefficients.\n","username":"sqrtX","reported":false,"is_thanked":false,"is_nothanked":false,"attachment":false,"thanks_received":0,"nothanks_received":0,"thankers":null,"deleted":false,"post_number":1,"post_time":1652819785,"num_edits":0,"post_format":"bbcode","last_edit_time":0,"last_editor_username":"","last_edit_reason":"","admin":false,"avatar":"\/\/avatar.artofproblemsolving.com\/avatar_355854.png","num_posts":344,"editable":false,"deletable":false,"show_from_start":true,"show_from_end":false}],"topic_id":2846853,"comment_count":2,"num_deleted":0,"topic_title":"Putnam 1970 A1","target_url":"","target_text":"","topic_type":"forum","state":"none","first_post_id":25229502,"first_poster_id":355854,"first_post_time":1652819785,"first_poster_name":"sqrtX","last_post_time":1653066635,"first_poster_avatar":"\/\/avatar.artofproblemsolving.com\/avatar_355854.png","last_poster_avatar":"\/\/avatar.artofproblemsolving.com\/avatar_574587.png","last_post_id":25250049,"last_poster_id":574587,"last_poster_name":"maxjw91","last_update_time":1653066635,"category_id":7,"is_public":true,"roles":{"432":"mod","93494":"mod","67223":"mod","9049":"mod","242520":"mod"},"tags":[{"tag_id":441,"tag_text":"Putnam","is_visible":true},{"tag_id":298,"tag_text":"function","is_visible":true},{"tag_id":194,"tag_text":"trigonometry","is_visible":true},{"tag_id":96815,"tag_text":"power series","is_visible":true}],"can_have_source":true,"locked":false,"forum_locked":0,"announce_type":"none","announce_through":"","announce_factor":0,"preview":"Show that the power series for the function
\nwhere ,<\/span> has either no zero coefficients or infinitely many zero coefficients.
\n","category_name":"College Math","category_main_color":"#511e8f","category_secondary_color":"#f2e6fe","num_reports":0,"poll_id":0,"source":"Putnam 1970","category_num_users":5,"category_num_topics":102698,"category_num_posts":402685,"num_views":78,"cat_can_target":0,"has_thanks":true,"has_nothanks":false,"is_bookmarked":false,"in_feed":false,"is_watched":false},"2822357":{"num_posts":3,"posts_data":[{"post_id":24942736,"topic_id":2822357,"poster_id":142747,"post_rendered":"Reduce each equation,![\"$1$\"](\"\/\/latex.artofproblemsolving.com\/d\/c\/e\/dce34f4dfb2406144304ad0d6106c5382ddd1446.png\")
<\/span> through ![\"$3$\"](\"\/\/latex.artofproblemsolving.com\/7\/c\/d\/7cde695f2e4542fd01f860a89189f47a27143b66.png\")
,<\/span>to standard form. Then find the coordinates of the center ,the vertices , and the foci.
\n![\"$1)x^2+xy+y^2+2x-2y=0$\"](\"\/\/latex.artofproblemsolving.com\/3\/4\/a\/34a1b2b56eef892795b093bab812ca9c9c57a0e2.png\")
\n![\"$2)x^2-4xy+4y^2+5\\sqrt5{y}+1=0$\"](\"\/\/latex.artofproblemsolving.com\/1\/6\/3\/163561fd6261567ec4e8aa27119c97abfb9648b1.png\")
\n![\"$3)x^2+4xy+y^2-4x+8y+\\frac{2}{3}=0$\"](\"\/\/latex.artofproblemsolving.com\/e\/0\/8\/e08f6b08e8d9ff74adc2cd44db7c86c7a5085441.png\")
","post_canonical":"Reduce each equation,$1$ through $3$,to standard form. Then find the coordinates of the center ,the vertices , and the foci.\n$1)x^2+xy+y^2+2x-2y=0$\n$2)x^2-4xy+4y^2+5\\sqrt5{y}+1=0$\n$3)x^2+4xy+y^2-4x+8y+\\frac{2}{3}=0$","username":"yt12","reported":false,"is_thanked":false,"is_nothanked":false,"attachment":false,"thanks_received":1,"nothanks_received":0,"thankers":"ImSh95","deleted":false,"post_number":1,"post_time":1649748245,"num_edits":0,"post_format":"bbcode","last_edit_time":0,"last_editor_username":"","last_edit_reason":"","admin":false,"avatar":"\/\/avatar.artofproblemsolving.com\/avatar_142747.png","num_posts":678,"editable":false,"deletable":false,"show_from_start":true,"show_from_end":false}],"topic_id":2822357,"comment_count":3,"num_deleted":0,"topic_title":"Conic (Find equation in standard form)","target_url":"","target_text":"","topic_type":"forum","state":"none","first_post_id":24942736,"first_poster_id":142747,"first_post_time":1649748245,"first_poster_name":"yt12","last_post_time":1653064808,"first_poster_avatar":"\/\/avatar.artofproblemsolving.com\/avatar_142747.png","last_poster_avatar":"\/\/avatar.artofproblemsolving.com\/avatar_92334.jpg","last_post_id":25249877,"last_poster_id":92334,"last_poster_name":"vanstraelen","last_update_time":1653071337,"category_id":7,"is_public":true,"roles":{"432":"mod","93494":"mod","67223":"mod","9049":"mod","242520":"mod"},"tags":[{"tag_id":29605,"tag_text":"conic","is_visible":true},{"tag_id":251,"tag_text":"analytic geometry","is_visible":true},{"tag_id":116,"tag_text":"calculus","is_visible":true},{"tag_id":228,"tag_text":"ellipse","is_visible":true},{"tag_id":229,"tag_text":"hyperbola","is_visible":true},{"tag_id":48,"tag_text":"geometry","is_visible":true},{"tag_id":169,"tag_text":"algebra","is_visible":true}],"can_have_source":true,"locked":false,"forum_locked":0,"announce_type":"none","announce_through":"","announce_factor":0,"preview":"Reduce each equation,<\/span> through ,<\/span>to standard form. Then find the coordinates of the center ,the vertices , and the foci.
\n
\n
\n","category_name":"College Math","category_main_color":"#511e8f","category_secondary_color":"#f2e6fe","num_reports":0,"poll_id":0,"source":"","category_num_users":5,"category_num_topics":102698,"category_num_posts":402685,"num_views":126,"cat_can_target":0,"has_thanks":true,"has_nothanks":false,"is_bookmarked":false,"in_feed":false,"is_watched":false},"1652146":{"num_posts":3,"posts_data":[{"post_id":10453587,"topic_id":1652146,"poster_id":281882,"post_rendered":"If ![\"$G$\"](\"\/\/latex.artofproblemsolving.com\/6\/e\/2\/6e28ce12d49d39f160d5a0ef54077fc98e4b9d2b.png\")
is a graph of order such that for all distinct nonadjacent vertices ![\"$u$\"](\"\/\/latex.artofproblemsolving.com\/9\/a\/d\/9ad99798ec4c38e165cf517cb9e02b1c9e824103.png\")
and ,<\/span>
\n![\"$$d_{G}(u)](\"\/\/latex.artofproblemsolving.com\/3\/c\/1\/3c186807ba7ca94b416da3e53fef6109ceca0712.png\")
then is hamiltonian-connected(i.e. any two nonadjacent vertices are connected with hamiltonian path).","post_canonical":"If $G$ is a graph of order $n$ such that for all distinct nonadjacent vertices $u$ and $v$,\n$$d_{G}(u) + d_{G}(v) \\ge n + 1,$$\nthen $G$ is hamiltonian-connected(i.e. any two nonadjacent vertices are connected with hamiltonian path).\n ","username":"mard","reported":false,"is_thanked":false,"is_nothanked":false,"attachment":false,"thanks_received":0,"nothanks_received":0,"thankers":null,"deleted":false,"post_number":1,"post_time":1527868823,"num_edits":0,"post_format":"bbcode","last_edit_time":0,"last_editor_username":"","last_edit_reason":"","admin":false,"avatar":"\/\/avatar.artofproblemsolving.com\/avatar_281882.png","num_posts":4,"editable":false,"deletable":false,"show_from_start":true,"show_from_end":false}],"topic_id":1652146,"comment_count":3,"num_deleted":0,"topic_title":"Graph Theory","target_url":"","target_text":"","topic_type":"forum","state":"none","first_post_id":10453587,"first_poster_id":281882,"first_post_time":1527868823,"first_poster_name":"mard","last_post_time":1653060801,"first_poster_avatar":"\/\/avatar.artofproblemsolving.com\/avatar_281882.png","last_poster_avatar":"\/\/avatar.artofproblemsolving.com\/avatar_270065.png?t=1647592393","last_post_id":25249454,"last_poster_id":270065,"last_poster_name":"CeuAzul","last_update_time":1653060801,"category_id":7,"is_public":true,"roles":{"432":"mod","93494":"mod","67223":"mod","9049":"mod","242520":"mod"},"tags":[{"tag_id":240,"tag_text":"graph theory","is_visible":true},{"tag_id":442,"tag_text":"college contests","is_visible":true}],"can_have_source":true,"locked":false,"forum_locked":0,"announce_type":"none","announce_through":"","announce_factor":0,"preview":"If is a graph of order such that for all distinct nonadjacent vertices and ,<\/span>
\nthen is hamiltonian-connected(i.e. any two nonadjacent vertices are connected with hamiltonian path).
\n","category_name":"College Math","category_main_color":"#511e8f","category_secondary_color":"#f2e6fe","num_reports":0,"poll_id":0,"source":"","category_num_users":5,"category_num_topics":102698,"category_num_posts":402685,"num_views":214,"cat_can_target":0,"has_thanks":true,"has_nothanks":false,"is_bookmarked":false,"in_feed":false,"is_watched":false}};AoPS.preload_topics[10]={"2848713":{"num_posts":2,"posts_data":[{"post_id":25249521,"topic_id":2848713,"poster_id":221021,"post_rendered":"Have the "Keep Learning" problems been discontinued? There hasn't been anything new there for a few months.","post_canonical":"Have the \"Keep Learning\" problems been discontinued? There hasn't been anything new there for a few months.","username":"sdpandit","reported":false,"is_thanked":false,"is_nothanked":false,"attachment":false,"thanks_received":1,"nothanks_received":0,"thankers":"ImSh95","deleted":false,"post_number":1,"post_time":1653061362,"num_edits":0,"post_format":"bbcode","last_edit_time":0,"last_editor_username":"","last_edit_reason":"","admin":false,"avatar":"\/\/avatar.artofproblemsolving.com\/avatar_221021.png","num_posts":2295,"editable":false,"deletable":false,"show_from_start":true,"show_from_end":false}],"topic_id":2848713,"comment_count":2,"num_deleted":0,"topic_title":"Keep Learning","target_url":"","target_text":"","topic_type":"forum","state":"closed","first_post_id":25249521,"first_poster_id":221021,"first_post_time":1653061362,"first_poster_name":"sdpandit","last_post_time":1653062542,"first_poster_avatar":"\/\/avatar.artofproblemsolving.com\/avatar_221021.png","last_poster_avatar":"\/\/avatar.artofproblemsolving.com\/avatar_219683.png?t=1607040961","last_post_id":25249632,"last_poster_id":219683,"last_poster_name":"devenware","last_update_time":1653062542,"category_id":10,"is_public":true,"roles":{"473145":"mod","500529":"mod","481507":"mod","470423":"mod"},"tags":[{"tag_id":758462,"tag_text":"keeplearning","is_visible":true},{"tag_id":5,"tag_text":"\/closed","is_visible":false}],"can_have_source":false,"locked":false,"forum_locked":0,"announce_type":"none","announce_through":"","announce_factor":0,"preview":"Have the "Keep Learning" problems been discontinued? There hasn't been anything new there for a few months.","category_name":"Site Support","category_main_color":"#a90008","category_secondary_color":"#ffe4e1","num_reports":0,"poll_id":0,"source":"","category_num_users":4,"category_num_topics":16579,"category_num_posts":138067,"num_views":43,"cat_can_target":0,"has_thanks":true,"has_nothanks":false,"is_bookmarked":false,"in_feed":false,"is_watched":false},"2848712":{"num_posts":2,"posts_data":[{"post_id":25249489,"topic_id":2848712,"poster_id":883469,"post_rendered":"Hi all,
\nI'm trying to edit an AoPS wiki page and I'm logged in, yet I can't edit it because AoPS thinks I'm not logged into the wiki for some stupid reason.
\nPlease help!
\nThanks!","post_canonical":"Hi all,\nI'm trying to edit an AoPS wiki page and I'm logged in, yet I can't edit it because AoPS thinks I'm not logged into the wiki for some stupid reason.\nPlease help!\nThanks!","username":"hastapasta","reported":false,"is_thanked":false,"is_nothanked":false,"attachment":false,"thanks_received":0,"nothanks_received":0,"thankers":null,"deleted":false,"post_number":1,"post_time":1653061152,"num_edits":0,"post_format":"bbcode","last_edit_time":0,"last_editor_username":"","last_edit_reason":"","admin":false,"avatar":"\/\/avatar.artofproblemsolving.com\/avatar_883469.jpeg?t=1641503781","num_posts":68,"editable":false,"deletable":false,"show_from_start":true,"show_from_end":false}],"topic_id":2848712,"comment_count":2,"num_deleted":1,"topic_title":"Why can't I edit the wiki when I'm logged in?","target_url":"","target_text":"","topic_type":"forum","state":"closed","first_post_id":25249489,"first_poster_id":883469,"first_post_time":1653061152,"first_poster_name":"hastapasta","last_post_time":1653061674,"first_poster_avatar":"\/\/avatar.artofproblemsolving.com\/avatar_883469.jpeg?t=1641503781","last_poster_avatar":"\/\/avatar.artofproblemsolving.com\/avatar_944981.png?t=1649452110","last_post_id":25249549,"last_poster_id":944981,"last_poster_name":"jlacosta","last_update_time":1653061685,"category_id":10,"is_public":true,"roles":{"473145":"mod","500529":"mod","481507":"mod","470423":"mod"},"tags":[{"tag_id":45137,"tag_text":"Bug","is_visible":true},{"tag_id":5,"tag_text":"\/closed","is_visible":false},{"tag_id":30967,"tag_text":"help","is_visible":true},{"tag_id":104956,"tag_text":"technical difficulties","is_visible":true}],"can_have_source":false,"locked":true,"forum_locked":0,"announce_type":"none","announce_through":"","announce_factor":0,"preview":"Hi all,
\nI'm trying to edit an AoPS wiki page and I'm logged in, yet I can't edit it because AoPS thinks I'm not logged into the wiki for some stupid reason.
\nPlease help!
\nThanks!","category_name":"Site Support","category_main_color":"#a90008","category_secondary_color":"#ffe4e1","num_reports":0,"poll_id":0,"source":"","category_num_users":4,"category_num_topics":16579,"category_num_posts":138067,"num_views":54,"cat_can_target":0,"has_thanks":true,"has_nothanks":false,"is_bookmarked":false,"in_feed":false,"is_watched":false},"2848334":{"num_posts":4,"posts_data":[{"post_id":25245172,"topic_id":2848334,"poster_id":593425,"post_rendered":"Hello! I know how to do this: Click to reveal hidden text<\/span>
\n
\nOnline Monmouth Math Competition!
\n
\n
\nUse the link http:\/\/www.ommcofficial.org\/<\/a> or https:\/\/ommc-website.vercel.app\/<\/a>. Check out our shiny new website with all the important information you need!<\/b>
\n
\nThis is not a local competition; any student 18 or younger anywhere in the world can attend. We have changed some elements of our contest format, so read this announcement carefully and thoroughly! Our website is currently down but we will let you know when it gets back up. Thanks for your understanding!<\/b>
\n
\nYou may have seen our earlier hype announcement<\/a>. We will still be posting on that thread with Problem of the Months and new video releases. But this is where we will post all updates about the competition.
\n
\nWhen is this?
\n<\/b>
\nThe test will be released on May 27th and will be due on June 5th<\/b>, tentatively (10 days to work on it). Mark your calendars!
\n
\nWho runs this?
\n<\/b>
\nThe Online Monmouth Math Competition (OMMC) for short was founded by a school friend (TempestGamer327) as well as myself. Later, a fellow WOOT classmate billert stepped up as well to help manage the competition and arrange a partnership with another student-run STEM educational organization, Buzzonline (buzzonline.org). Together, we are the three OMMC directors and have worked tirelessly to bring this contest to fruition. We also cannot thank our fellow staff members enough for the work and effort they have put into this organization as well. As of now, we also provide a monthly resource via the Problem of the Month, as well as some Youtube content coming soon. You can find some of this on this AoPS thread: https:\/\/artofproblemsolving.com\/community\/c5h2731203<\/a>
\n
\nWhat happened in OMMC Year 1?
\n<\/b>
\nOMMC Year 1 was for the most part a big success! We had 230+ participants from around the world take part in the competition, and the winners came away with hundreds of dollars in prizes! Questions were high quality and the test went smoothly.
\n
\nIs this going to be exactly the same as OMMC Year 2?
\n<\/b>
\nChange is good! We\u2019re dramatically switching things up for OMMC Year 2. We\u2019re going to have one single team round with 25 questions, and teams can be up to 4 people.<\/b> The test is untimed<\/b>: you\u2019re going to have around a week to work on the problems with your team. Most importantly, the questions are just going to be better this time around.
\n
\nHow are the problems?
\n<\/b>
\nOnly the best problems by our panel of dedicated and talented problem writers have been selected. Hundreds of problems have been comprehensively reviewed by our panel of equally wonderful testsolvers. Our content creation staff has achieved pretty much every mathematical achievement possible! Staff members have qualified for AIME, excelled at USAMO and USAJMO, and attended MOP.<\/b> Our staff members have contributed to countless student-led math organizations and competitions<\/b> in the past and we all have a high degree of mathematical experience under our belt. I believe that OMMC Year 2 contains some of our best work yet.
\n
\nHere are sample problems that we encourage prospective contestants to try.
\n
\nhttps:\/\/artofproblemsolving.com\/community\/c2825027<\/a>
\n
\nOr, check out the problems from last year\u2019s contest:
\n
\nhttps:\/\/artofproblemsolving.com\/community\/c1976711<\/a>
\n
\nSome high quality mock contests that have been contributed to by OMMC Staff Members include SADGIME<\/a>, POGIME<\/a>, and AAMC<\/a>. Other contests staff members have contributed heavily to include ADMC<\/a> and OYMC<\/a>.
\n
\nHow hard is it?
\n<\/b>
\nWe have designed the test to be accessible to beginners at the early end but also challenging to experts on the late end. The early questions will be around the difficulty of easy questions from the AMC 10\/12. Later questions will be at or exceeding the difficulty of the hardest questions from the AIME. We hope that teams will collaborate and think deeply about the problems on the test.
\n
\nHow do we sign up?
\n<\/b>
\nYou won\u2019t have to! You\u2019ll just put in your information as you submit the test, since it\u2019s untimed. However, we do encourage you to \u201csign up\u201d on this thread, just like how you might with a mock contest. This isn\u2019t required to take the test nor does it force you to take the test. But it\u2019s a great way to show support for us and bump the thread to the top of the forums, so we do appreciate it!
\n
\nHow will the test be held?
\n<\/b>
\nWe highly recommend competitors join our Community Discord<\/b> for the latest updates on the competition, as well as for finding team members to team up with. However, all the important information will also be updated on this thread as necessary. Each team can consist of between 1 and 4 people, inclusive. Each competitor in a team has to be 18 or younger to be eligible for the competition.<\/b>
\n
\nSolo participants are allowed and will be treated simply as one man teams. They will be eligible for the same prizes as teams with multiple people.
\n
\nOur test will be held completely online and untimed. There will be one single test of 25 questions that all members of the team can access. Each question has a nonnegative integer answer. Each question is weighted equally, so each team will receive a single score out of 25.
\n
\nAs for what is allowed, we do not allow the use of anything other than writing utensils, scratch paper, compass, ruler\/straightedge, and a single four function calculator (addition, subtraction, multiplication, division). In particular, the use of websites such as Wolfram Alpha, Geogebra, Symbolab, and\/or Desmos is not allowed. Competitors can only communicate about the test with the people in their team. Collaboration between teams or between a team and an individual not on the team, is prohibited. If we find any violations of academic integrity, we will disqualify all teams involved.
\n
\nTiebreaker rounds will be given out if necessary after the contest period has ended. We will contact teams through email for this.
\n
\nOn May 27th, we\u2019ll put out a link by which teams can register and access the test. Teams will put in their registration information as they submit the test. For now, we recommend competitors to search for team members and join the OMMC Discord Community for further updates.
\n
\nPrizes?
\n<\/b>
\nPrizes shouldn\u2019t be the main reason someone takes OMMC, but in previous years we have been sponsored by organizations such as AoPS, Maplesoft, and Wolfram Alpha, who have provided hundreds of dollars to top scoring competitors.
\n
\nThis year, we have a 45 dollar Desmos Gift Card Code, 300 dollars in gift cards and T-shirts from Jane Street, a 500 dollar Geogebra Webinar, 100 dollars in AoPS coupons, and 3600 dollars in Wolfram Alpha Notebook Editions to give out so far. We are happy to announce that Maplesoft will be sponsoring us with $168 value in 4 Maple Learn Premium accounts, active for 6 months, that will be given to the winning team. More updates on prizes coming soon. <\/b>
\n
\nSome of these prizes will be raffled out! You just need to put in a submission to be eligible.<\/b> Spread the news and keep the signups going, you do NOT want to miss this opportunity!
\n
\nI have more questions. Who do I ask?
\n<\/b>
\nWe respond most quickly on our community discord, but you can also contact us through email via the ommcofficial@gmail.com address.
\n
\nWe hope for your participation, and good luck!
\n<\/b>
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be a convex quadrilateral, the incenters of and are ,<\/span> respectively. It is known that concurrent at a point .<\/span> The line perpendicular to through intersects with the outer angle bisector of and the outer angle bisector at ,<\/span> respectively. Show that .<\/span>","post_canonical":"Let $ABCD$ be a convex quadrilateral, the incenters of $\\triangle ABC$ and $\\triangle ADC$ are $I,J$, respectively. It is known that $AC,BD,IJ$ concurrent at a point $P$. The line perpendicular to $BD$ through $P$ intersects with the outer angle bisector of $\\angle BAD$ and the outer angle bisector $\\angle BCD$ at $E,F$, respectively. 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\nEvaluate the integral of u<\/b>. dr<\/b>
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\nEvaluate the integral of u<\/b>. dr<\/b>
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