MathDB
2015 BMT Team 14

Source:

January 6, 2022
combinatorics

Problem Statement

Alice is at coordinate point (0,0)(0, 0) and wants to go to point (11,6)(11, 6). Similarly, Bob is at coordinate point (5,6)(5, 6) and wants to go to point (16,0)(16, 0). Both of them choose a lattice path from their current position to their target position at random (such that each lattice path has an equal probability of being chosen), where a lattice path is defined to be a path composed of unit segments with orthogonal direction (parallel to x-axis or y-axis) and of minimal length. (For instance, there are six lattice paths from (0,0)(0, 0) to (2,2)(2, 2).) If they walk with the same speed, find the probability that they meet.
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