# Sunday Times Teaser 3009 – Head Count

*by Victor Bryant*

#### Published Sunday May 24 2020 (link)

My grandson and I play a simple coin game. In the first round we toss seven coins and I predict how many “heads” there will be whilst my grandson predicts the number of “tails”. After the tossing I score a point for each head plus a bonus of ten if my prediction was correct — my grandson scores likewise for the tails. We then repeat this with six coins, then five, and so on down to a single coin. After each round we keep cumulative totals of our scores. In one game, for over half of the pairs of cumulative scores, my grandson’s total was like mine but with the digits in reverse order. In fact he was ahead throughout and at one stage his cumulative total was double mine — and he had an even bigger numerical lead than that on just one earlier occasion and one later occasion.

List the number of heads in each of the seven rounds.

Simple manual solution:

For each section(7,6,5 etc) there’s an ongoing total of the number of heads & tails. The last digit is different for each section, unaffected by any bonuses.

We need at least 3 sections that end with a reversible pair of numbers. Only possible if the sum of that pair has a last digit that matches the above. This only works for 3 sections, the others are easily filled in following the teaser rules.- total number of bonuses can only stay the same or go up.

Error in above! We need at least 4 sections that end in a reversible pair. It only works for 4 sections. Mea Culpa