Use pigeonhole principle to solve please: will upvote! Let V = {v1,…,vk} be any set of...

Use pigeonhole principle to solve please: will upvote!

Let V = {v1,…,vk} be any set of vectors in R^2 (Real Numbers to the power of 2). Suppose n agents each start at (0,0) and each takes a mV-walk where a mV-walk consists of a sequence of exactly m steps and each step moves the agent along a vector in V. Prove that, if n > (m + k − 1 , k − 1) (these are two separate terms in one parenthesis), then some pair of agents finishes their walk at the same location.

Expert Solution

Colby Messinger answered 3 days ago

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