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arrangements of 0 and 1 on each square of a 4 x 4 board

Source: Mexican Mathematical Olympiad 1995 OMM P6

July 28, 2018
boardcombinatorics

Problem Statement

A 11 or 00 is placed on each square of a 4×44 \times 4 board. One is allowed to change each symbol in a row, or change each symbol in a column, or change each symbol in a diagonal (there are 1414 diagonals of lengths 11 to 44). For which arrangements can one make changes which end up with all 00s?
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