$\underline{\text { Avilov N.I. }}$.

In the vertices of a 33-gon, integers from 1 to 33 were written in some order. Then, on each side, the sum of the numbers at its ends was written.

Can the sides contain 33 consecutive integers (in some order)?
Let the numbers at the vertices go in the following order: $1,18,2,19,3,20, \ldots, 16,33,17$. It is not hard to verify that the sums of two adjacent numbers will increase in order from 19 to 50. And the sum of the first and last is 18.

## Answer

They can.