Enigma 422: Keeping fit by halves
10 November 2017
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From New Scientist #1572, 6th August 1987 [link]
In our local sports club everyone plays at least one of badminton, squash and tennis. Of those who don’t play badminton, half play squash. Of those who don’t play squash, half play badminton. Of those who play badminton and squash, half play tennis.
I play badminton only: there are two more players who play tennis only than there are who play badminton only.
If a player plays just two of the three games, then his or her spouse also plays just two of the three games.
The membership consists entirely of married couples and each of the three games is played by at least one member of each married couple.
How many people are there in the club, and how many of those play all three games?