Five positive whole numbers have a mean of 10, a median of 8 and a single mode of 6. What is the largest value the biggest of them can take?

Explanation

1. 01

   Write them in order as a, b, 8, d, e. Their total is $5 \times 10 = 50$.

2. 02

   6 must appear at least twice and is below the median, so $a = b = 6$. Then $d + e = 50 - 20 = 30$.

3. 03

   d cannot be 8 (8 would tie 6 as a mode) and cannot equal e (another tie), so the smallest d is 9.

4. 04

   Hence the largest possible e is $30 - 9 = 21$.