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Operations on a grid

Source: CWMO 2012 Q7

October 1, 2012
combinatorics proposedcombinatorics

Problem Statement

Let nn be a positive integer ≥2\geq 2 . Consider a nn by nn grid with all entries 11. Define an operation on a square to be changing the signs of all squares adjacent to it but not the sign of its own. Find all nn such that it is possible after a finite sequence of operations to reach a nn by nn grid with all entries −1-1
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