The arithmetic mean of ten different natural numbers is 15. Find the greatest value of the greatest of these numbers.

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Evaluation. The sum of these numbers is 150. Since all numbers are distinct, the sum of the nine smallest of them is no less than $1+2+\ldots+9=45$. Therefore, the largest number cannot be greater than 105.

Example: $(1+2+\ldots+9+105): 10=15$.

## Answer

105.