MathDB
2004 General, part 2 #10

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March 8, 2024
combinatorics

Problem Statement

A lattice point is a point whose coordinates are both integers. Suppose Johann walks in a line from the point (0,2004)(0, 2004) to a random lattice point in the interior (not on the boundary) of the square with vertices (0,0)(0, 0), (0,99)(0, 99), (99,99)(99,99), (99,0)(99, 0). What is the probability that his path, including the endpoints, contains an even number of lattice points?
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