This website contains problems from math contests. Problems and corresponding tags were obtained from the Art of Problem Solving website.

Tags were heavily modified to better represent problems.

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Found problems: 3

1961 Putnam, A1
Tags: intersection of set , analytic geometry
The graph of the equation $x^y =y^x$ in the first quadrant consists of a straight line and a curve. Find the coordinates of the intersection of the line and the curve.

1959 Putnam, B1
Tags: intersection of set , line
Let each of $m$ distinct points on the positive part of the $x$-axis be joined to $n$ distinct points on the positive part of the $y$-axis. Obtain a formula for the number of intersection points of these segments, assuming that no three of the segments are concurrent.

1954 Putnam, B3
Tags: interval , intersection of set
Let $[a_1 , b_1 ] , \ldots, [a_n ,b_n ]$ be a collection of closed intervals such that any of these closed intervals have a point in common. Prove that there exists a point contained in every one of these intervals.