5. There is a $6 \times 6$ square, all cells of which are white. In one move, it is allowed to change the color of both cells in any domino (a rectangle of two cells) to the opposite. What is the minimum number of moves required to obtain a square with a checkerboard pattern? Don't forget to explain why a smaller number of moves would not be enough.
Answer: 18 moves.

Solution. Note that in the chessboard coloring of a $6 \times 6$ square, there are 18 black cells. At the same time, no two of them can be turned black in one move, because they are not covered by one domino. Therefore, at least 18 moves are required (at least one move per cell). This can be done in 18 moves, for example, by dividing the board into 9 squares of $2 \times 2$, and in each square, first recoloring the bottom domino, and then the right one. There are other algorithms as well.

Criteria. Only the answer - 1 point, correctly formulated algorithm - 5 points. Full solution 7 points.