Task 7.2

Can a two-digit and a three-digit number be formed from the digits $1,2,3,4,5$ such that the second number is divisible by the first? Each digit must be used exactly once.

Number of points 7
Answer:

It is possible.

## Solution

It is easy to check that 532 is divisible by 14, and 215 is divisible by 43.

To find these pairs, we can apply a brute-force approach. To reduce the number of options, we use divisibility properties, which in particular imply that: if a two-digit number ends in 5, the second number cannot be divisible by it; if the first number is even, then the second must also be even; if the first number is divisible by 9, the second cannot be divisible by it.

## Additional Criteria for Checking

- “7" - any two correct pairs
- " 4 " - one correct pair
- " 0 " - the problem is not solved or solved incorrectly