B1. Both the rows and columns of an $8 \times 8$ chessboard are numbered from $1$ to $8$. On each square of the chessboard, a number of grains of wheat is placed that is equal to the product of the row number and the column number.

How many grains of wheat are there in total on the chessboard?
B1. 1296 In the first column, from top to bottom, there are sequentially $1 \times 1, 1 \times 2, 1 \times 3, \ldots, 1 \times 8$ grains of wheat.

In total, in the first column: $\quad 1 \times (1+2+3+4+5+6+7+8)$.

In the second column, there are: $\quad 2 \times (1+2+3+4+5+6+7+8)$.

In the third column, there are: $\quad 3 \times (1+2+3+4+5+6+7+8)$.

In the eighth column, finally: $\quad 8 \times (1+2+3+4+5+6+7+8)$.

In total, therefore: $(1+2+3+4+5+6+7+8) \times (1+2+3+4+5+6+7+8)$.

Since $1+2+3+4+5+6+7+8=\frac{1}{2} \times 8 \times (1+8)=36$, in total thus $36^{2}=1296$ grains of wheat.