Look at the cells a1, b2, c3, d4, a4, d1. At the begining we have that they are white and in one move we change the colour of exactly one of those cells.It means that the number of moves is even. On the other hand, if we look at the cells b1, c2, a3, d3, b4, we obtain that number of moves is odd. Contradiction.

den_thewhitelion wrote: We have a 4x4 board.All 1x1 squares are white.A move is changing colours of all squares of a 1x3 rectangle from black to white and from white to black.It is possible to make all the 1x1 squares black after several moves? Colour the board as shown below. Note that in each move an equal number of red, blue and green squares are changed. But there aren’t an equal number of red and green squares. So, it isn’t possible to make all the squares white. $\blacksquare$

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