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2023 MOAA Gunga P22

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October 15, 2023
MOAA 2023

Problem Statement

Harry the knight is positioned at the origin of the Cartesian plane. In a "knight hop", Harry can move from the point (i,j)(i,j) to a point with integer coordinates that is a distance of 5\sqrt{5} away from (i,j)(i,j). What is the number of ways that Harry can return to the origin after 6 knight hops?
Proposed by Harry Kim
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