Problem #9

Two ants A and B are at opposite corners of an 8×8 grid. Ant A starts at the southwest corner and ant B at the northeast corner. Ant A moves at a constant speed along the edges of the grid, but can only move to the north or east. Ant B moves at the same speed, but can only move to the south or west. If all pairs of paths are equally likely, what is the probability that the ants meet? For example, although the two paths shown below cross, the ants do not actually meet.

Generalize to an a×b grid.

The solution will be posted shortly.

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