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

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Found problems: 3

1954 Putnam, B3
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.
interval intersection of set algebra

1959 Putnam, B1
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.
intersection of set line algebra

1961 Putnam, A1
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.
intersection of set analytic geometry algebra combinatorics