olymmath

HMMT 2010 U19

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A 5-dimensional ant starts at one vertex of a 5 -dimensional hypercube of side length 1 . A move is when the ant travels from one vertex to another vertex at a distance of 2\sqrt{2} away. How many ways can the ant make 5 moves and end up on the same vertex it started at?

Dataset text NuminaMath olympiads. Quoted with source.

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