Sunday Times Teaser 3146 – Curling League
by John Owen
Published Sunday January 08 2023
In our curling league (between 4 and 26 teams), each team plays each other once. Teams are ranked according to the number of wins (draws are impossible). If any teams are tied on wins, ranking is only possible if those teams have different numbers of wins in their mutual games. For example, in a three-way tie if A beats B, B beats C and A beats C, the ranking is ABC, but if C beats A (or A has not yet played C), then ranking is impossible, as A and B have one win each.
At one point (each team had played G games), ranking the teams as above was possible. However, if each team had played G-1 games, a ranking would have been impossible, irrespective of results. With one more team in the league, the minimum number of games needed to allow a ranking is G+2.
How many teams are in the league and what was the value of G?