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Problem #265

Meeting probability
 Public ★(x8) 08/25/15 by sinan 10xp Math 80.0%

There is a grid of roads (MxN). Two people, one at A (0,0) and the other at B (N,M), start to walk from A to B and B to A respectively at the same time. They both walk the shortest path to their destination. For instance, if you come from B to A, you must always move from East to West (left) or North to South (down).

The man at B walks faster than the one at A by a factor of k.
(vB=k*vA where k>1)

If they walk in any possible direction equally likely on a 19x23 grid, what is the probability that they meet each other on their way if k is equal to 4/3 (1) or 6/5 (2)?

Example:
Answer=5/14,5/28 for k=2 and k=3/2 on 3x3 grid.

The following shows a possible meeting for k=2:



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