Problem Set Workbook
Access the downloadable workbook for 2001 USAMO problems here.
Discussion Forum
Engage in discussion about the 2001 USAMO math contest by visiting Random Math USAMO 2001 Forum
Individual Problems and Solutions
For problems and detailed solutions to each of the 2001 USAMO problems, please refer below:
Problem 1: Each of eight boxes contains six balls. Each ball has been colored with one of colors, such that no two balls in the same box are the same color, and no two colors occur together in more than one box. Determine, with justification, the smallest integer for which this is possible.
Solution:
Problem 2: Let be a triangle and let be its incircle. Denote by and the points where is tangent to sides and , respectively. Denote by and the points on sides and , respectively, such that and , and denote by the point of intersection of segments and . Circle intersects segment at two points, the closer of which to the vertex is denoted by . Prove that .
Solution:
Problem 3: Let , and be nonnegative real numbers such that
Prove that
Solution:
The problems on this page are the property of the MAA's American Mathematics Competitions