7.1. Can the positive integers $1 \sim 16$ be placed in the 16 squares of a $4 \times 4$ grid so that the sums of the numbers in each row and each column are exactly 8 consecutive integers?
7.1. Not possible.

Assuming it can be done, the sum of the sums of each row and each column should be twice the sum of the numbers in the table, which is $16 \times 17$. However, the equation $k+(k+1)+\cdots+(k+7)=16 \times 17$ has no integer solution.