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- 14:12, 5 September 2020 2020 CAMO Problems/Problem 1 (hist) [667 bytes] Jbala (talk | contribs) (Created page with "==Problem 1== Let <math>f:\mathbb R_{>0}\to\mathbb R_{>0}</math> (meaning <math>f</math> takes positive real numbers to positive real numbers) be a nonconstant function such t...")
- 14:07, 5 September 2020 2020 CAMO Problems (hist) [4,281 bytes] Jbala (talk | contribs) (Created page with "==Day 1== ===Problem 1=== Let <math>f:\mathbb R_{>0}\to\mathbb R_{>0}</math> (meaning <math>f</math> takes positive real numbers to positive real numbers) be a nonconstant fun...")
- 12:39, 5 September 2020 2020 CAMO (hist) [601 bytes] Jbala (talk | contribs) (Created page with "The '''first USAMO''' was held January 10 through February 3, 2020. The first link contains the full set of test problems. The rest contain each individual problem and its...")
- 12:37, 5 September 2020 CAMO Problems and Solutions (hist) [207 bytes] Jbala (talk | contribs) (Created page with "CAMO problems and solutions. *2020 CAMO == See also == * Christmas Math Competitions * CMC Problems and Solutions * Mathematics competition resources ...")
- 00:47, 5 September 2020 2020 CIME II (hist) [1,144 bytes] Jbala (talk | contribs) (Created page with "'''2020 CIME II''' problems and solutions. The test was held on Friday, February 7, 2020. The first link contains the full set of test problems. The rest contain each...")
- 00:35, 5 September 2020 2020 CMC 12B Answer Key (hist) [29 bytes] Jbala (talk | contribs) (Created page with "DBBDC DCDAD ABDAA CBDDB CDDED")
- 00:31, 5 September 2020 2020 CMC 12A Answer Key (hist) [29 bytes] Jbala (talk | contribs) (Created page with "CCBCA DCADC BDDCD CDCDC CCACB")
- 00:28, 5 September 2020 2020 CMC 12B Problems (hist) [33 bytes] Jbala (talk | contribs) (Created page with "{{CMC12 Problems|year=2020|ab=B}}")
- 00:24, 5 September 2020 2020 CMC 12B (hist) [1,603 bytes] Jbala (talk | contribs) (Created page with "'''2020 CMC 12B''' problems and solutions. The test was held on Sunday, January 26, 2020. *2020 CMC 12B Problems *2020 CMC 12B Answer Key **2020 CMC 12B Problems/Pr...")
- 00:19, 5 September 2020 2020 CMC 12A Problems (hist) [33 bytes] Jbala (talk | contribs) (Created page with "{{CMC12 Problems|year=2020|ab=A}}")
- 00:13, 5 September 2020 2020 CMC 12A (hist) [1,601 bytes] Jbala (talk | contribs) (Created page with "'''2020 CMC 12A''' problems and solutions. The test was held on Friday, December 27, 2019. *2020 CMC 12A Problems *2020 CMC 12A Answer Key **2020 CMC 12A Problems/P...")
- 00:11, 5 September 2020 CMC 12 Problems and Solutions (hist) [186 bytes] Jbala (talk | contribs) (Created page with "CMC 12 problems and solutions. {| class="wikitable" style="text-align:center" |- ! Year || Test A || Test B |- | 2020 || CMC 12A || 2020 CMC 12B | C...")
- 22:41, 4 September 2020 Harmonic Bundles (hist) [16 bytes] Rudolf1279 (talk | contribs) (Created page with "Harmonic Bundles")
- 11:58, 1 September 2020 2020 CIME I Problems/Problem 15 (hist) [523 bytes] Jbala (talk | contribs) (Created page with "==Problem 15== Find the number of integer sequences <math>a_1, a_2, \ldots, a_6</math> such that :(1) <math>0 \le a_1 < 6</math> and <math>12 \le a_6 < 18</math>, :(2) <math>1...")
- 11:55, 1 September 2020 2020 CIME I Problems/Problem 14 (hist) [947 bytes] Jbala (talk | contribs) (Created page with "==Problem 14== Let <math>ABC</math> be a triangle with sides <math>AB = 5, BC = 7, CA = 8</math>. Denote by <math>O</math> and <math>I</math> the circumcenter and incenter of...")
- 11:49, 1 September 2020 2020 CIME I Problems/Problem 13 (hist) [648 bytes] Jbala (talk | contribs) (Created page with "==Problem 13== Chris writes on a piece of paper the positive integers from <math>1</math> to <math>8</math> in that order. Then, he randomly writes either <math>+</math> or <m...")
- 16:20, 31 August 2020 2020 CIME I Problems/Problem 12 (hist) [505 bytes] Jbala (talk | contribs) (Created page with "==Problem 12== Define a sequence <math>a_0, a_1, a_2, ...</math> by <cmath>a_i=\underbrace{1\ldots1}_{2^{i}\text{ 1's}}\underbrace{0\ldots0}_{(2^i-1)\text{ 0's}}1_2,</cmath> w...")
- 16:14, 31 August 2020 2020 CIME I Problems/Problem 11 (hist) [755 bytes] Jbala (talk | contribs) (Created page with "==Problem 11== An <math>excircle</math> of a triangle is a circle tangent to one of the sides of the triangle and the extensions of the other two sides. Let <math>ABC</math> b...")
- 13:19, 31 August 2020 Christmas Invitational Mathematics Examination (hist) [2,892 bytes] Jbala (talk | contribs) (Created page with "The '''Christmas Invitational Mathematics Examination''' ('''CIME'''), like the ('''AIME'''), is the second exam in the series of exams used to challenge bright students on th...")
- 11:35, 31 August 2020 2020 CIME I Problems/Problem 10 (hist) [453 bytes] Jbala (talk | contribs) (Created page with "==Problem 10== Let <math>1=d_1<d_2<\cdots<d_k=n</math> be the divisors of a positive integer <math>n</math>. Let <math>S</math> be the sum of all positive integers <math>n</ma...")
- 11:33, 31 August 2020 2020 CIME I Problems/Problem 9 (hist) [3,829 bytes] Jbala (talk | contribs) (Created page with "==Problem 9== Let <math>ABCD</math> be a cyclic quadrilateral with <math>AB=6, AC=8, BD=5, CD=2</math>. Let <math>P</math> be the point on <math>\overline{AD}</math> such that...")
- 11:33, 31 August 2020 2020 CIME I Problems/Problem 8 (hist) [1,021 bytes] Jbala (talk | contribs) (Created page with "==Problem 8== A person has been declared the first to inhabit a certain planet on day <math>N=0</math>. For each positive integer <math>N=0</math>, if there is a positive numb...")
- 11:26, 31 August 2020 2020 CIME I Problems/Problem 7 (hist) [516 bytes] Jbala (talk | contribs) (Created page with "==Problem 7== For every positive integer <math>n</math>, define <cmath>f(n)=\frac{n}{1 \cdot 3 \cdot 5 \cdots (2n+1)}.</cmath> Suppose that the sum <math>f(1)+f(2)+\cdots+f(20...")
- 11:21, 31 August 2020 2020 CIME I Problems/Problem 6 (hist) [918 bytes] Jbala (talk | contribs) (Created page with "==Problem 6== Find the number of complex numbers <math>z</math> satisfying <math>|z|=1</math> and <math>z^{850}+z^{350}+1=0</math>. ==Solution== {{solution}} {{CIME box|year...")
- 22:27, 30 August 2020 CMC Problems and Solutions (hist) [295 bytes] Jbala (talk | contribs) (Created page with "You can find problems and solutions from the math contests run by the Christmas Mathematics Competitions on the following pages: *CIME Problems and Solutions")
- 22:05, 30 August 2020 2020 CIME I Problems/Problem 5 (hist) [1,438 bytes] Jbala (talk | contribs) (Created page with "==Problem 5== Let <math>ABCD</math> be a rectangle with sides <math>AB>BC</math> and let <math>E</math> be the reflection of <math>A</math> over <math>\overline{BD}</math>. If...")
- 21:59, 30 August 2020 2020 CIME I Problems/Problem 4 (hist) [740 bytes] Jbala (talk | contribs) (Created page with "==Problem 4== There exists a unique positive real number <math>x</math> satisfying <cmath>x=\sqrt{x^2+\frac{1}{x^2}} - \sqrt{x^2-\frac{1}{x^2}}.</cmath> Given that <math>x</ma...")
- 21:51, 30 August 2020 2020 CIME I Problems/Problem 3 (hist) [800 bytes] Jbala (talk | contribs) (Created page with "==Problem 3== In a math competition, all teams must consist of between <math>12</math> and <math>15</math> members, inclusive. Mr. Beluhov has <math>n > 0</math> students and...")
- 21:34, 30 August 2020 2020 CIME I Problems/Problem 2 (hist) [1,386 bytes] Jbala (talk | contribs) (Created page with "==Problem 2== At the local Blast Store, there are sufficiently many items with a price of <math>\$n.99</math> for each nonnegative integer <math>n</math>. A sales tax of <math...")
- 20:38, 30 August 2020 2020 CIME I Problems/Problem 1 (hist) [1,380 bytes] Jbala (talk | contribs) (Created page with "==Problem 1== A knight begins on the point <math>(0,0)</math> in the coordinate plane. From any point <math>(x,y)</math> the knight moves to either <math>(x+2,y+1)</math> or <...")
- 13:59, 30 August 2020 2020 CIME I Problems (hist) [7,165 bytes] Jbala (talk | contribs) (Created page with "{{CIME Problems|year=2020|n=I}} ==Problem 1== A knight begins on the point <math>(0,0)</math> in the coordinate plane. From any point <math>(x,y)</math> the knight moves to e...")
- 13:27, 30 August 2020 2020 CIME I Answer Key (hist) [74 bytes] Jbala (talk | contribs) (Created page with "#252 #020 #480 #014 #192 #100 #312 #176 #023 #418 #209 #048 #225 #093 #302")
- 13:23, 30 August 2020 CIME Problems and Solutions (hist) [744 bytes] Jbala (talk | contribs) (Created page with "This is a list of all CIME exams in the AoPSWiki. Some of them contain complete questions and solutions, others complete questions, and others are lacking both questi...")
- 13:16, 30 August 2020 2020 CIME I (hist) [1,127 bytes] Jbala (talk | contribs) (Created page with "'''2020 CIME I''' problems and solutions. The test was held on Friday, January 3, 2020. The first link contains the full set of test problems. The rest contain each i...")
- 23:35, 28 August 2020 1955 AHSME Problems/Problem 38 (hist) [1,199 bytes] Angrybird029 (talk | contribs) (Created page with "== Problem 38== Four positive integers are given. Select any three of these integers, find their arithmetic average, and add this result to the fourth integer. Thus the numb...")
- 11:45, 28 August 2020 Thomas Jefferson High School for Science and Technology ARML (hist) [7 bytes] Mathlete0825 (talk | contribs) (Created page with "They OP")
- 00:03, 28 August 2020 ACT (hist) [21 bytes] Welcomesk2001 (talk | contribs) (ads)
- 13:24, 27 August 2020 Dihedral group (hist) [653 bytes] Duck master (talk | contribs) (created page)
- 13:10, 27 August 2020 1998 JBMO Problems/Problem 3 (hist) [1,167 bytes] Duck master (talk | contribs) (Created page with "Find all pairs of positive integers <math>(x,y)</math> such that <cmath>x^y = y^{x - y}.</cmath> == Solution == Note that <math>x^y</math> is at least one. Then <math>y^{x -...")
- 23:54, 26 August 2020 DELETE (hist) [30 bytes] Rf20008 (talk | contribs) (Created page with "text deleted")
- 19:16, 24 August 2020 The World’s Largest Countdown Round (hist) [5 bytes] Marble3 (talk | contribs) (Created page with "hello")
- 12:27, 23 August 2020 2004 IMO Problems/Problem 5 (hist) [388 bytes] Pureswag (talk | contribs) (Created page with "In a convex quadrilateral <math>ABCD</math>, the diagonal <math>BD</math> bisects neither the angle <math>ABC</math> nor the angle <math>CDA</math>. The point <math>P</math> l...")
- 12:26, 23 August 2020 2004 IMO Problems/Problem 6 (hist) [203 bytes] Pureswag (talk | contribs) (Created page with "We call a positive integer alternating if every two consecutive digits in its decimal representation are of different parity. Find all positive integers <math>n</math> which h...")
- 12:25, 23 August 2020 2004 IMO Problems/Problem 3 (hist) [259 bytes] Pureswag (talk | contribs) (Created page with "Define a “hook” to be a figure made up of six unit squares as shown in this picture: http://bit.ly/IMO2004P1, or any of the figures obtained by applying rotations and refl...")
- 12:22, 23 August 2020 2010 AMC 12A Problems Raw (hist) [0 bytes] Firebolt360 (talk | contribs) (Created page with "== Problem 1 == What is <math>\left(20-\left(2010-201\right)\right)+\left(2010-\left(201-20\right)\right)</math>? <math>\textbf{(A)}\ -4020 \qquad \textbf{(B)}\ 0 \qquad \tex...")
- 12:21, 23 August 2020 2005 IMO Problems/Problem 5 (hist) [638 bytes] Pureswag (talk | contribs) (Created page with "Let <math>ABCD</math> be a fixed convex quadrilateral with <math>BC = DA</math> and <math>BC \nparallel DA</math>. Let two variable points <math>E</math> and <math>F</math> li...")
- 12:19, 23 August 2020 2005 IMO Problems/Problem 2 (hist) [346 bytes] Pureswag (talk | contribs) (Created page with "Let <math>a_1, a_2, \dots</math> be a sequence of integers with infinitely many positive and negative terms. Suppose that for every positive integer <math>n</math> the numbers...")
- 12:15, 23 August 2020 2005 IMO Problems/Problem 3 (hist) [180 bytes] Pureswag (talk | contribs) (Created page with "Let <math>x, y, z > 0</math> satisfy <math>xyz\ge 1</math>. Prove that <cmath>\frac{x^5-x^2}{x^5+y^2+z^2} + \frac{y^5-y^2}{x^2+y^5+z^2} + \frac{z^5-z^2}{x^2+y^2+z^5} \ge 0.</c...")
- 12:05, 23 August 2020 2005 IMO Problems/Problem 1 (hist) [432 bytes] Pureswag (talk | contribs) (Created page with "Six points are chosen on the sides of an equilateral triangle <math>ABC</math>: <math>A_1, A_2</math> on <math>BC</math>, <math>B_1</math>, <math>B_2</math> on <math>CA</math>...")
- 02:23, 23 August 2020 2021 AIME II Problems (hist) [46 bytes] Greatmather (talk | contribs) (Created page with "did you really expect the problems to be here?")