7. In the calculation
$$
H E \times E H=W H E W,
$$
where different letters stand for different nonzero digits. Find the values of all the letters.
7. We have
$$
E H \times H E=W H E W=W \times 1001+10 \times H E .
$$

Hence
$$
H E \times(E H-10)=W \times 1001=W \times 7 \times 11 \times 13 .
$$

Since $E \neq H, H E$ is not divisible by 11 , hence $E H-10$ is divisible by 11 , whence $E-1=H$. Now $H E$ is a multiple of 13 with consecutive digits, hence it is 78 . Then $W=6$ and the unique reconstruction is
$$
78 \times 87=6786 .
$$