6. Variant 1. Grisha thought of such a set of 10 different natural numbers that their arithmetic mean is 16. What is the maximum possible value of the largest of the numbers he thought of?
Answer: 115.

Solution: The sum of the given numbers is $10 \cdot 16=160$. Since all the numbers are distinct, the sum of the 9 smallest of them is no less than $1+2+\cdots+9=45$. Therefore, the largest number cannot be greater than $160-45=115$. This is possible: $(1+2+\cdots+9+115): 10=16$.