The arithmetic mean of ten distinct natural numbers is 10. What is the maximum of these ten numbers?

Answer: the largest number of 10 numbers is 55.

Natural numbers are numbers obtained as a result of the natural counting of something whole. They must be positive and whole.

The arithmetic mean is the sum of several numbers divided by the number of these numbers.

If we know the arithmetic mean and the number of numbers, then their sum will be:

10 * 10 = 100.

We need to find the maximum possible number in this amount. This means that the other 9 terms should be minimal, but not repeated according to the conditions of the problem. This is only possible with this option:

1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 = 45.

Let’s calculate the last 10th term, which will be as large as possible for the given conditions:

100 – 45 = 55.