Sunday Times Teaser 2724 – Headcount

by Victor Bryant

A game I play with my grandson has six rounds. In round one, seven coins are tossed, in round two, six, in round three, five, and so on, down to two coins in round six. On each round I then get a number of points equal to the number of heads and my grandson gets a number of points equal to the number of tails. But, before each round, we each predict our score and gain an extra ‘bonus’ of a fixed number of points (less than 40) when our predictions are correct.

In one game we noticed that, at the end of each round, the combined total of our points so far had always been a prime number.

How much is the bonus and what was the sum of our scores at the end of this game?