User contributions
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- 18:44, 18 July 2016 (diff | hist) . . (+662) . . N 1987 USAMO Problems/Problem 5 (Created page with "== Problem == <math>a_1, a_2, \cdots, a_n</math> is a sequence of 0's and 1's. T is the number of triples <math>(a_i, a_j, a_k)</math> with <math>i<j<k</math> which are not eq...") (current)
- 18:44, 18 July 2016 (diff | hist) . . (+411) . . N 1987 USAMO Problems/Problem 4 (Created page with "==Problem== M is the midpoint of XY. The points P and Q lie on a line through Y on opposite sides of Y, such that <math>|XQ| = 2|MP|</math> and <math>\frac{|XY|}2 < |MP| < \fr...") (current)
- 18:42, 18 July 2016 (diff | hist) . . (+393) . . N 1987 USAMO Problems/Problem 2 (Created page with "==Problem== The feet of the angle bisectors of <math>\Delta ABC</math> form a right-angled triangle. If the right-angle is at <math>X</math>, where <math>AX</math> is the bise...") (current)
- 18:42, 18 July 2016 (diff | hist) . . (+600) . . N 1987 USAMO Problems/Problem 3 (Created page with "==Problem== <math>X</math> is the smallest set of polynomials <math>p(x)</math> such that: : 1. <math>p(x) = x</math> belongs to <math>X</math>. : 2. If <math>r(x)</math> be...")
- 18:42, 18 July 2016 (diff | hist) . . (+4) . . m 1987 USAMO Problems (current)
- 18:31, 18 July 2016 (diff | hist) . . (-402) . . m 1987 USAMO Problems/Problem 1
- 18:29, 18 July 2016 (diff | hist) . . (+41) . . m 1987 USAMO Problems
- 18:29, 18 July 2016 (diff | hist) . . (-8) . . m 1987 USAMO (current)
- 14:51, 18 July 2016 (diff | hist) . . (-42) . . m User talk:1=2
- 14:51, 18 July 2016 (diff | hist) . . (+1,159) . . N 1986 USAMO Problems/Problem 5 (Created page with "== Problem == By a partition <math>\pi</math> of an integer <math>n\ge 1</math>, we mean here a representation of <math>n</math> as a sum of one or more positive integers wher...")
- 14:50, 18 July 2016 (diff | hist) . . (0) . . m 1986 USAMO Problems/Problem 4 (→See Also)
- 14:50, 18 July 2016 (diff | hist) . . (+800) . . N 1986 USAMO Problems/Problem 4 (Created page with "==Problem== Two distinct circles <math>K_1</math> and <math>K_2</math> are drawn in the plane. They intersect at points <math>A</math> and <math>B</math>, where <math>AB</math...")
- 14:49, 18 July 2016 (diff | hist) . . (0) . . m 1986 USAMO Problems/Problem 3
- 14:49, 18 July 2016 (diff | hist) . . (+495) . . 1986 USAMO Problems/Problem 3
- 14:48, 18 July 2016 (diff | hist) . . (-16) . . m 1986 USAMO Problems/Problem 2 (→See Also) (current)
- 14:48, 18 July 2016 (diff | hist) . . (+386) . . m 1986 USAMO Problems/Problem 2
- 14:45, 18 July 2016 (diff | hist) . . (+113) . . 1986 USAMO Problems/Problem 1
- 14:44, 18 July 2016 (diff | hist) . . (+41) . . m 1986 USAMO Problems
- 14:44, 18 July 2016 (diff | hist) . . (+41) . . m 1985 USAMO Problems (current)
- 14:43, 18 July 2016 (diff | hist) . . (-8) . . m 1986 USAMO (current)
- 13:03, 18 July 2016 (diff | hist) . . (+1,638) . . N 1985 USAMO Problems/Problem 5 (Created page with "== Problem == Let <math>a_1,a_2,a_3,\cdots</math> be a non-decreasing sequence of positive integers. For <math>m\ge1</math>, define <math>b_m=\min\{n: a_n \ge m\}</math>, that...") (current)
- 12:54, 18 July 2016 (diff | hist) . . (+553) . . N 1985 USAMO Problems/Problem 4 (Created page with "== Problem == There are <math>n</math> people at a party. Prove that there are two people such that, of the remaining <math>n-2</math> people, there are at least <math>\lfloor...")
- 12:54, 18 July 2016 (diff | hist) . . (+370) . . N 1985 USAMO Problems/Problem 3 (Created page with "== Problem == Let <math>A,B,C,D</math> denote four points in space such that at most one of the distances <math>AB,AC,AD,BC,BD,CD</math> is greater than <math>1</math>. Determ...")
- 12:53, 18 July 2016 (diff | hist) . . (+273) . . N 1985 USAMO Problems/Problem 2 (Created page with "== Problem == Determine each real root of <math>x^4-(2\cdot10^{10}+1)x^2-x+10^{20}+10^{10}-1=0</math> correct to four decimal places. ==Solution== {{solution}} == See Also...")
- 12:45, 18 July 2016 (diff | hist) . . (0) . . m 1985 USAMO Problems/Problem 1 (→See Also)
- 12:43, 18 July 2016 (diff | hist) . . (+427) . . N 1985 USAMO Problems/Problem 1 (Created page with "==Problem== Determine whether or not there are any positive integral solutions of the simultaneous equations <cmath>x_1^2+x_2^2+\cdots+x_{1985}^2=y^3, \hspace{20pt} x_1^3+x_...")
- 12:42, 18 July 2016 (diff | hist) . . (-8) . . m 1985 USAMO (current)
- 12:42, 18 July 2016 (diff | hist) . . (-12) . . m 1984 USAMO (→See Also) (current)
- 12:42, 18 July 2016 (diff | hist) . . (-12) . . m 1983 USAMO (→See Also) (current)
- 12:41, 18 July 2016 (diff | hist) . . (+4) . . m 1984 USAMO
- 12:40, 18 July 2016 (diff | hist) . . (+468) . . N 1984 USAMO Problems/Problem 5 (Created page with "== Problem == <math>P(x)</math> is a polynomial of degree <math>3n</math> such that <cmath>\begin{eqnarray*} P(0) = P(3) = \cdots &=& P(3n) = 2, \\ P(1) = P(4) = \cdots &=& P...")
- 12:35, 18 July 2016 (diff | hist) . . (+532) . . N 1984 USAMO Problems/Problem 4 (Created page with "== Problem == A difficult mathematical competition consisted of a Part I and a Part II with a combined total of <math>28</math> problems. Each contestant solved <math>7</math>...") (current)
- 12:33, 18 July 2016 (diff | hist) . . (+1) . . m 1984 USAMO Problems (→Problem 4) (current)
- 12:33, 18 July 2016 (diff | hist) . . (+485) . . N 1984 USAMO Problems/Problem 3 (Created page with "== Problem == <math>P</math>, <math>A</math>, <math>B</math>, <math>C</math>, and <math>D</math> are five distinct points in space such that <math>\angle APB = \angle BPC = \a...")
- 12:30, 18 July 2016 (diff | hist) . . (+39) . . m 1984 USAMO Problems (→Problem 3)
- 12:29, 18 July 2016 (diff | hist) . . (+691) . . m 1984 USAMO Problems/Problem 2
- 12:28, 18 July 2016 (diff | hist) . . (+1) . . m 1984 USAMO Problems/Problem 1 (→= Solution 2)
- 12:28, 18 July 2016 (diff | hist) . . (+6) . . m 1984 USAMO Problems/Problem 1 (→Solution)
- 12:26, 18 July 2016 (diff | hist) . . (+41) . . m 1984 USAMO Problems
- 12:25, 18 July 2016 (diff | hist) . . (+1) . . m 1983 USAMO Problems (current)
- 12:24, 18 July 2016 (diff | hist) . . (-14) . . m User talk:1=2 (→USA(J)MO)
- 00:02, 18 July 2016 (diff | hist) . . (+1,142) . . N 1983 USAMO Problems/Problem 5 (I'll leave my progress up for anyone who wants to finish the problem. I have a solution sketch in mind, but I need sleep now.)
- 23:20, 17 July 2016 (diff | hist) . . (0) . . m 1983 USAMO Problems/Problem 4 (→See Also)
- 23:19, 17 July 2016 (diff | hist) . . (-37) . . m 1983 USAMO Problems/Problem 4 (→Solution)
- 23:18, 17 July 2016 (diff | hist) . . (+4,995) . . N 1983 USAMO Problems/Problem 4 (Created page with "== Problem == Six segments <math>S_1, S_2, S_3, S_4, S_5,</math> and <math>S_6</math> are given in a plane. These are congruent to the edges <math>AB, AC, AD, BC, BD,</math> a...")
- 22:31, 17 July 2016 (diff | hist) . . (0) . . m 1983 USAMO Problems/Problem 3 (→See Also)
- 22:31, 17 July 2016 (diff | hist) . . (+399) . . N 1983 USAMO Problems/Problem 3 (Created page with "== Problem == Each set of a finite family of subsets of a line is a union of two closed intervals. Moreover, any three of the sets of the family have a point in common. Prove ...")
- 22:29, 17 July 2016 (diff | hist) . . (+137) . . m 1983 USAMO Problems/Problem 1 (→Problem) (current)
- 22:26, 17 July 2016 (diff | hist) . . (+1,189) . . 1983 USAMO Problems/Problem 1 (The solution page was poorly written, so it has been re-written.)
- 22:18, 17 July 2016 (diff | hist) . . (+1) . . m 1983 USAMO Problems
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