Sunday Times Teaser 2706 – Spinners

by Mike Fletcher

My friend and I play a game with three ‘spinners’, each of which allow the equally likely random selection of one of five positive (non-zero) whole numbers engraved on their faces. The sums of the numbers on each spinner are the same and two of them have the numbers (3, 3, 3, 3, 3) and (2, 2, 2, 3, 6).

My friend picks a spinner, I then pick one, we both spin our chosen spinners and the one with the highest number wins (or the game is drawn). Over many games it turns out that I am more likely to win no matter which spinner my friend chooses.

What are the numbers on the third spinner?