[ Divisibility of numbers. General properties ]  [ Pairing and grouping; bijections ]

Kolya claims that it is possible to determine whether the sum of all four-digit numbers, which do not contain the digits 0 or 9 in their representation, is divisible by 101, without calculating the sum itself. Is Kolya right?
A number paired with a number composed of the digits $a, b, c, d$ is a number composed of the digits $9-a, 9-b, 9-c, 9-$ $d$, placed in the same order. Thus, all four-digit numbers satisfying the given conditions are divided into pairs, the sum of the numbers in which is 9999. Therefore, the sum of all such numbers will be a multiple of $9999=$ $99 \cdot 101$.

## Answer

Correct.