A.K. Tolpygo

Ten numbers are written around a circle, their sum is 100. It is known that the sum of any three consecutive numbers is not less than 29.

Indicate the smallest number $A$ such that in any such set of numbers, each number does not exceed $A$.
Evaluation. Consider some single number $d$, and divide the other nine numbers into three pairs of adjacent numbers. The sum of these nine numbers is no less than 87, so $d \leq 13$. Therefore, in any set that meets the conditions, each number does not exceed 13.

Example. A set containing the number 13 exists: 10, 10, 9, 10, 10, 9, 10, 10, 9, 13.

## Answer

$A=13$.