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hexagon with analytic geometry, partitioned in squares

Source: Austrian Polish 1979 APMC

April 26, 2020
analytic geometrygridhexagonSquarescombinatorial geometrycombinatorics

Problem Statement

Let nn and mm be fixed positive integers. The hexagon ABCDEFABCDEF with vertices A=(0,0)A = (0,0), B=(n,0)B = (n,0), C=(n,m)C = (n,m), D=(n−1,m)D = (n-1,m), E=(n−1,1)E = (n-1,1), F=(0,1)F = (0,1) has been partitioned into n+m−1n+m-1 unit squares. Find the number of paths from AA to CC along grid lines, passing through every grid node at most once.
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