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Problem of the Week 819

Taxi!

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Consider the plane grid consisting of all vertical and horizontal lines in the plane lattice. There are many paths along these "streets" that are 20 units long and connect (0, 0) to (10, 10). How many paths of length 20 from (0, 0) to (10, 10) pass through (7, 1) and go through only intersections (i, j) with j < i (except for the two endpoints).

Source: Leo Schneider

© Copyright 1996 Stan Wagon. Reproduced with permission.

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