Prove the following:
Assume that the average of four integers (all integers are different) is 20. Prove that at least 1 of those 4 integers has to be greater than 21.
Proof:
We know that for average of 4 integers to be 20, the sum of those integers must be 80. With this in mind, we attempt to find the maximum sum of 4 different integers less than or equal to 21.
$\displaystyle
21 + 20 + 19 + 18 = 78$
and,
$\displaystyle 78 < 80$
Therefore, there is no combination of 4 different integers less than or equal to 21 that have an average of 20.