$\begin{aligned} & {[\text { Arithmetic operations. Numerical identities }]} \\ & {[\quad \underline{\text { Arithmetic. Mental calculation, etc. }}]}\end{aligned}$

The sum of six different natural numbers is 22. Find these numbers.
Consider the six smallest natural numbers: $1,2, \ldots, 6$. Note: among the desired numbers, there should be no equal numbers.

## Solution

Consider the six smallest natural numbers: $1,2, \ldots, 6$. Their sum is 21. This means that our initial equation will be achieved if we increase any of the numbers by 1. However, if we increase any number from 1 to 5, we will end up with two equal numbers among our numbers. This means that we need to increase the last number, i.e., take 7 instead of 6. As a result, we get the desired set $-1,2,3,4,5,7$.

## Answer

$1,2,3,4,5,7$.