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white cells in 8x8 chessboard

Source: Switzerland - 2018 Swiss MO Final Round p1

December 30, 2022
combinatoricsColoring

Problem Statement

The cells of an 8×88\times 8 chessboard are all coloured in white. A move consists in inverting the colours of a rectangle 1×31 \times 3 horizontal or vertical (the white cells become black and conversely). Is it possible to colour all the cells of the chessboard in black in a finite number of moves ?
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