223. Cryptarithm with multiplication. After performing regular multiplication "in column," a person replaced each even digit with the letter $E$, and each odd digit - with the letter $O^{*}$. As a result, the following expression was obtained:

| $O E E$  E  EOEE |
| :--- |
| EOE |
| $O O E E$ |

Restore the given multiplication completely.
223. Since $188 \cdot 8=1504$, the first $O$ must be greater than 1. After multiplying this $O$ by the first $E$ of the multiplier, the result should be $\leqslant 8$; thus, $O=3$, and $E=2$. Numbers of the form $3 E E$, which when multiplied by 2 give $E O E$, can only be $306, 308, 326, 328, 346$, and 348. But if we multiply these numbers by 4 and 6, in no case will we get an expression of the form $E O E E$. If, however, we multiply them by 8, then only the last two numbers will give an expression of the form $E O E E$. Further, $346 \cdot 28=9688$; therefore, the only solution is