As the Rugby World Cup is currently ongoing I thought I’d do a puzzle based on the scoring system. A kick (drop goal or penalty) is worth 3 points, an unconverted try is worth 5 points, and a converted try is worth 7 points.

Some scores are impossible to reach: you can’t get 1, 2 or 4.

8 is the first score that’s achievable in two ways, as long as we say that ‘3 then 5’ is different from ‘5 then 3’.

In how many ways is the score ‘23’ achievable?