The Six Nations rugby tournament is upon us, and here is a puzzle about that competition.
There are several ways teams can gain points in the league table, four points for winning and zero for losing, two points for a draw, a bonus point for scoring four tries, a bonus point for losing by seven points or fewer, and the grand slam bonus.
So across the whole competition, what is the lowest number of league points the six teams can amass, and what is the highest number of league points they can get?
Leaving aside bonus points, each game produces four points; a winning team gets four and the opponent gets zero, or a draw gets both teams two points. On that basis there are 15 games giving a total of 60 points, and that is the lowest total possible.
To get the highest total we must include as many bonus points as possible.
If both teams score four tries in all 15 games that gives another 30 points. And if every game is won by seven points or fewer then 15 teams get losing bonus points which is another 15.
Finally, if one team wins all its games, a grand slam, it gets three more bonus points, making a total of 48 bonus points.
This gives a highest possible total of 108. The range from 60 to 108 is surprisingly large.