**The Problem Center**

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[Archive]**

**To propose a problem, please send an email to the moderators, with a short
title.**

**The Problems:**

**POLYA037:2005 International Mathematical Olympiad (Merida, Mexico) and solutions by Jean-Pierre Ehrmann**

**POLYA036: 2003 William Putnam Lowell Mathematical Competition B-Problems****(last update: 12/8/03)**

**POLYA035: 2003 William Putnam Lowell Mathematical Competition A-Problems****(last update: 12/8/03)**

**POLYA034: 2002 William Putnam Lowell Mathematical Competition B-Problems****(last update: 12/16/02)****POLYA033: 2002 William Putnam Lowell Mathematical Competition A-Problems****(last update: 12/16/02)**

**POLYA032: Sum of cubes of Pellian Numbers (proposed by Jose Luis Diaz-Barrero; last update: 11/22/02).**-
**POLYA031: A combinatorial sum (proposed by Luis Lopes; last update: 11/25/02)** -
**POLYA030: Congruent circles tangent to BAC and BIC (proposed by Antreas P. Hatzipolakis; last update: 8/12/02).** -
**POLYA029: 2002 International Mathematical Olympiad (Glasgow) (last update: 8/6/02)** -
**POLYA028: A functional equation (proposed by Stephen C. Locke; last update: 3/4/02)** -
**POLYA027: Probability of winning a solitaire card game (proposed by Antreas P. Hatzipolakis; last update: 3/1/02)** -
**POLYA026: Common chord of circles (proposed by Antreas P. Hatzipolakis; last update: 2/7/02)** -
**POLYA025: Maximum sum of arithmetic progressions (proposed by Paul Yiu; last update: 1/11/02)** -
**POLYA024: Long descent to zero (proposed by Li Zhou; last update: 3/22/02)** -
**POLYA023: Relation on graphs from games (proposed by Stephen C. Locke; last update: 1/5/02)** -
**POLYA022: Triangle centers constructible from O, H, I (proposed by Paul Yiu; last update: 12/6/02)** -
**POLYA021: Adding lots of Egyptian fractions (proposed by Len M. Smiley; last update: 12/7/01)** -
**POLYA020: Chomp (proposed by Stephen C. Locke; last update: 12/6/01)** -
**POLYA019: Plane sets containing reflections of points in lines (proposed by Jean-Pierre Ehrmann; last update: 12/5/01)** -
**POLYA018: 2001 William Putnam Lowell Mathematical Competition B-Problems (last update: 12/7/01)** -
**POLYA017: 2001 William Putnam Lowell Mathematical Competition A-Problems (last update: 12/4/01)** -
**POLYA016: Iteration of sums of Fibonacci divisors (proposed by Antreas P. Hatzipolakis; last update: 12/1/01)** -
**POLYA015: Circle tangent to an ellipse contained in a rectangle (proposed by Paul Yiu; last update: 11/29/01)** -
**POLYA014: Square as a sum of two factorials (proposed by Lev Emelyanov; last update: 11/26/01)** -
**POLYA013: Length of non-periodic part of decimal expansion of 1/N (proposed by Luis Lopes; last update: 11/21/01)** -
**POLYA012: The Feuerbach point is the perspector (proposed by Tatiana Emelyanova; last update: 11/20/01)** -
**POLYA011: Points on a conic (proposed by Jean-Pierre Ehrmann; last update: 11/20/01)** -
**POLYA010: Integers of the form bc/a + ca/b + ab/c (proposed by Floor van Lamoen; last update: 11/16/01)** -
**POLYA009: 3 by 3 magic square with distinct square entries (proposed by Lev Emelyanov; last update: 2/22/02)** -
**POLYA008: First n for which m^n < n! (proposed by Floor van Lamoen; last update: 12/27/01)** -
**POLYA007: Amount that cannot be paid in bills of m and n dollars (proposed by Luis Lopes; last update: 12/3/01)** -
**POLYA006: Construction of triangle ABC with given A, a, and sum of altitudes (proposed by Antreas P. Hatzipolakis; last update:11/20/01)** -
**POLYA005: Traces 1,2,3,... (proposed by Stephen C. Locke; 11/30/01)** -
**POLYA004: Functions with smooth square and cube (proposed by Xiaodong Zhang; last update: 11/27/01)** -
**POLYA003: Integers of the form a/(bc) + b/(ca) + c/(ab) (proposed by Jean-Pierre Ehrmann; last update: 11/15/01)** -
**POLYA002: Integer pairs (x,y) for which (x^2+y^2)/(1+pxy) is an integer (proposed by Jean-Pierre Ehrmann; last update: 12/3/01)** -
**POLYA001: Degree n Polynomial P(x) with x^(n+1)P(x)-1 divisible by (x-1)^(n+1) (proposed by Paul Yiu; last update: 11/9/01)**