308. A simple "game". In the following cryptarithm

| $M A T H$ |
| :--- |
| $M A G S$ |
| $M A T H$ |
| GAME |

the word $G A M E^{*}$ is used instead of some prime number. Find this number.
308. The letter $M$ must represent one of the elements of the set $\{1,2,3\}$, the letter $A$ one of the elements of the set $\{4,5,9\}$, from which it follows that the letter $G$ coincides with some element of the set $\{4,7,8\} . .^{*}$ Looking at the table of prime numbers, we will find that the only suitable prime number can be only 8923.

After this, it is already easy to decipher the entire cryptarithm:

![](https://cdn.mathpix.com/cropped/2024_05_21_2b40d984baf9da275c68g-184.jpg?height=252&width=714&top_left_y=1773&top_left_x=677)

$[C$. Diano, M. M., 43, 227 (May 1970).]