The purpose of this game is to fill the board with the squares of only red color. By clicking a square you change the color of all the squares, that are in the same row and column with the clicked square.

You can see here a starting position for which this game doesn't have a solution.

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It follows from the system of linear equations that corresponds to this game that a solution exists if and only if the number of white squares in each row and column is odd or in each row and column is even. For this puzzle this obviously not true.

We also can prove that it is impossible to solve this puzzle without any equations. We only need to notice that each time when we click at a square we change the number of white squares by 1 in each row and column. So if we had odd number of white squares at some row or column then after clicking we will have even and viceversa. So we see that we always will have different number of white squares in second and third row. So we never fill the whole board by red squares.