Gribalko A.V.

On a $10 \times 10$ checkerboard, there is a bacterium in one of the cells. In one move, the bacterium moves to an adjacent cell and splits into two (both remain in the same cell). Then, one of the bacteria on the board moves to an adjacent cell and splits into two, and so on. Can it happen that after several such moves, there are an equal number of bacteria in all cells?
We will color the cells of the board in white and black in a checkerboard pattern. Consider the difference between the number of bacteria on white cells and the number of bacteria on black cells. When moving from a black cell to a white one, this difference increases by 3, and when moving from a white cell to a black one, it decreases by 3. Since initially this difference was 1 or -1, it will never become a multiple of 3, in particular, it will never become 0.

## Answer

no.