Yatsenko I.V.

Vanya thought of a simple three-digit number, all digits of which are different.

What digit can it end with if its last digit is equal to the sum of the first two?
Use the divisibility rules for 2, $2,3$.

## Solution

Obviously, the last digit is greater than 1. A three-digit prime number cannot end in an even digit (i.e., $0,2,4,6$ or 8), nor in the digit 5. If the last digit is 3 or 9, then the sum of all the digits of the number, which is twice the last digit, is divisible by 3, and thus the number itself is divisible by 3. Therefore, the only remaining digit is seven.

## Answer

By 7.

## Problem