### Instruction: The mean of four distinct positive integers is 5. If the largest of these four integers is 13, what is the smallest of the four integers?### Response: The mean of four distinct positive integers is 5, which means that the sum of the four integers is 4 times 5, or 20.
If the largest of the four integers is 13, then the other three integers must add up to 20 - 13, or 7.
Since the other three integers are distinct and positive, they must be 1, 2, and 4, in some order.
Therefore, the smallest of the four integers is 1.