4. In the record of three two-digit numbers, there are no zeros, and in each of them, both digits are different. Their sum is 41. What could be their sum if the digits in them are swapped?
Answer: 113.

Solution. In all numbers, the tens digit is 1. Otherwise, the largest is at least 21, and the other two are at least 12. Their sum is no less than $12+12+21=44$, which is not equal to 41. The sum of the units digits is 11 (zeros are not allowed). Therefore, the sum with the digits rearranged is 113.

There are five possible sets of three numbers: $12,12,17$ or $12,13,16$, or 12, 14, 15 or 13, 13, 15 or 13, 14, 15. (This can justify the answer)

Criteria. Answer with one or two, three or four examples: 1 point.

Answer with five examples, but without proof that there are no others: 2 points.

## Full solution: 7 points.