## 1. Smaller Number

The sum of two three-digit numbers, all six of whose digits are mutually distinct, is 1000. What is the maximum value that the smaller of these two numbers can have?

Result: $\quad 498$
## Solution.

Since 1000 : $2=500$, the smaller number will be less than 500.

Let's start with the first number less than 500 with all different digits. This is 498.

It holds that $498+502=1000$, and 502 and 498 have all different digits, so the answer is 498.