Chernyaev N.L.

In each cell of an $8 \times 8$ board, a natural number is written. It turns out that for any cutting of the board into dominoes, the sums of the numbers in all the dominoes are different. Can it be that the largest number written on the board is no more than 32?
Let's record ones in the black cells, and all numbers from 1 to 32 in the white cells. With any domino tiling, each domino will contain exactly one white and one black cell. Therefore, the sums in the dominoes will be $2,3, \ldots$, 33.

## Answer

It can.