Net Loss (Sunday 26th Oct Puzzle)
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Reminder of the question: Alice, Bob and Claire want to play table tennis. Since there is only one table and two bats, they decide that whoever loses a game steps out for the next game to let the other person in. The players of the first game are chosen randomly. By the end of their session, Alice has played 17 games, Bob 15 and Claire 10. Who lost the second game?
1) Given the three players played 10 + 15 + 17 = 42 games between them and there are 2 player per game we know there were 42/2 = 21 games played in total
2) Given Claire played 10 games, and she must play in alternate games, she cannot have played in game 1
3) Given Claire only played 10 games, she cannot have won any of her games as this would result in her playing in consecutive games and reaching a total of more than 10
4) Therefore game 2 was lost by Claire (in fact she lost all games she participated in)
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