Five whole numbers have a mean of 20, a median of 21 and a range of 12. What is the largest possible value of the biggest number?

Explanation

1. 01

   In order: a, b, 21, d, e with $e = a + 12$ and a total of 100.

2. 02

   So $a + b + d + (a + 12) = 79$, i.e. $2a + b + d = 67$.

3. 03

   To make e big, make a big. The least b and d can be are a and 21: $2a + a + 21 \le 67$ gives a ≤ 15.

4. 04

   With $a = 15$: $b = 15$, $d = 22$, $e = 27$. Check: $15 + 15 + 21 + 22 + 27 = 100$.