Nikola had one three-digit and one two-digit number. Each of these numbers was positive and composed of mutually different digits. The difference between Nikola's numbers was 976.

What was their sum?

(L. Hozová)

Hint. Which three-digit numbers are possible?
The largest three-digit number with distinct digits is 987. If this were one of Niko's numbers, the other would have to be 11 (to make the difference 976). This is a two-digit number, but it is not composed of distinct digits, so it could not have been Niko's number.

The next smaller three-digit number with distinct digits is 986. If this were one of Niko's numbers, the other would have to be 10. This is a two-digit number with distinct digits, so it could be a possible Niko's number.

No other pair is feasible, as 10 is the smallest two-digit number. Niko's numbers were 986 and 10, so their sum was 996.

Notes. One can also consider from the smallest two-digit number: If one of Niko's numbers was 10, the other would have to be 986 (to make the difference 976). This is a three-digit number with distinct digits, so it could be a possible Niko's number. For other two-digit numbers with distinct digits (12, 13, 14, 15, ...), the second number would either contain two identical digits (988, 989, 990, 991, ...) or would not be a three-digit number (for two-digit numbers greater than 23). Therefore, 10 and 986 were Niko's numbers.

It is not difficult to identify the suitable pair of numbers. Part of the problem is also the analysis of other possibilities, i.e., the justification that there are no more such pairs. A solution without a proper analysis cannot be rated at the highest level.

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