If 5 numbers have an average of 20 and none of the five is less than 15, what is the greatest possible value of any one of them?

The five add to $5\times 20=100$. One number is as large as possible when the other four are as small as possible, and the floor of 15 lets them go no lower, so the other four total 60 and the largest is 100 - 60 = 40. 25 mirrors the 5-unit gap below the average as a 5-unit gap above it, but a floor on four numbers does not cap the fifth by the same amount. 85 holds only one other number at 15 and forgets the remaining three. 100 is the total of all five, which one number could reach only if the other four were 0.