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2023 MOAA Speed P8

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October 13, 2023
MOAA 2023

Problem Statement

In the coordinate plane, Yifan the Yak starts at (0,0)(0,0) and makes 1111 moves. In a move, Yifan can either do nothing or move from an arbitrary point (i,j)(i,j) to (i+1,j)(i+1,j), (i,j+1)(i,j+1) or (i+1,j+1)(i+1,j+1). How many points (x,y)(x,y) with integer coordinates exist such that the number of ways Yifan can end on (x,y)(x,y) is odd?
Proposed by Yifan Kang
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