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This is Saturday night mathematics, yet, it is not an absurd exercise The French premier league has 20 teams. After 38 matches (all teams meeting each other twice), the last 3 by point total are relegated to the next division. Points are acquired by the following rule: win 3, draw 1, lose 0.

The heuristic rule is that 43 is the magic number, namely a teams reaching 43 points will not be relegated. My question is, is this true? Of course the number comes from historical observation, not a computation, but the real threshold number is in principle computable.

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By no means! If each team wins once and loses once against each opponent, then every team will end up with 57 points, and the relegated teams will be decided by goal difference.

If you don't want goal difference to be a factor, then have three of the teams exchange one of their wins for a draw. These teams will end up on 55 points, and will all be relegated.

TonyK
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    If two teams make no points, everyone else gets twelve points from them and 51 from each other, for 63 points. – Empy2 Oct 23 '15 at 00:49