Today Puzzle #541
Puzzle No. 541 鈥� Thursday 8 August
The Premiership season starts tomorrow. Twenty clubs will play each other twice, with 3 points awarded for a victory and one for a draw. The bottom three clubs will be relegated. At the outset, before a match has been played, how many points does a club need to be mathematically certain of avoiding relegation?
Today’s #PuzzleForToday has been set by Peter Kellner former President of YouGov
Click here for the answer
The answer is 64. If the bottom TWO clubs lose all their matches against the other 18, they will obviously be relegated. Suppose the other 18 clubs win one match and lose the other against each other – as well as winning their four matches against the bottom two. Then, the end of season table will show:
Top 18 clubs: 17 wins and 17 defeats against each other, plus four wins against the bottom two = 21 wins, 17 defeats = 21x3 = 63 points.
The club with the best goal difference will be champions, while that with the worst goal difference will be relegated.
In order to avoid this theoretical danger, a club needs 63+1 points = 64
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