Math CentralQuandaries & Queries


Question from Peter:

I see your formula for 16 players 4 rounds.
Is it possible to get the players into different groups each day.
E.G Player 1 in group 1 the first day,
Group 2 the second day,
Group 3 the third day,
Group 4 the fourth day.
Then so on through the players.


Not perfectly. Let's think about what happens with the four players who are in group 1 on the first day. If all four of them are in groups 2, 3 and 4 on any other day, then two of them must be in the same group (again). The same is true for the players in groups 2, 3 and 4. So no matter what you do, if no pair is together twice then on each day there at least 4 players who are in the same group number as a previous day.


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