### Instruction: The average of four different positive whole numbers is $4.$ If the difference between the largest and smallest of these numbers is as large as possible, what is the average of the other two numbers?### Response: The average of four numbers is 4, so their sum must be 4 times 4, or 16.
If the difference between the largest and smallest numbers is as large as possible, then the smallest number must be 1 and the largest number must be 13.
(This is because the other two numbers have to be positive whole numbers, and 1 and 13 are the only such numbers that add up to 14, leaving 2 for the other two numbers.)
Now, the average of the other two numbers is just their sum divided by 2.
Since their sum is 16 - 1 - 13 = 2, their average is 2/2 = 1.