Badminton progressions
A game of badminton is won by the first player to win 21 points, except if the score reaches 20-20, in which case it continues until one player is two points ahead. A match is won by the first player to win two games.
In this match each player won one of the first two games, so that the match required a third game to determine the result. For each of the players, the number of points they won in the three games, taken in game order, formed an arithmetic progression (with a non-zero common difference).
What…
