Problem

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Tags: combinatorics unsolved, combinatorics



The squares of an n*n chessboard (n >1) are filled with 1s and -1s. A series of steps are performed. For each step, the number in each square is replaced with the product of the numbers that were in the squares adjacent. Find all values of n for which, starting from an arbitrary collection of numbers, after finitely many steps one obtains a board filled with 1s.