Name: Diana

Question:
I have 12 pairs playing bridge against one another for 12 games. I need to have each pair partnered with another pair -- but only once. I'm looking for a schedule for play for all 12 games. They should only be able to play against another team only once also. (ex: 1/2 v 3/4 then 4/2 v 3/1) Thank you for this opportunity to solve my dilemma.

Hi Diana,

Twelve pairs, playing against each other only once, make 11 games, not 12. However it is possible to arrange 11 nights so that each pair plays against all others precisely once. The simplest pattern is as follows: on the k-th night, pair 12 is matched against pair k, then the remaining pairs starting from k clockwise are matched in order against the remaining pairs starting from k counterclockwise:

Night 1: 12 vs 1, 2 vs 11, 3 vs 10, 4 vs 9, 5 vs 8, 6 vs 7.

Night 2: 12 vs 2, 3 vs 1, 4 vs 11, 5 vs 10, 6 vs 9, 7 vs 8.

Night 3: 12 vs 3, 4 vs 2, 5 vs 1, 6 vs 11, 7 vs 10, 8 vs 9.

Night 4: 12 vs 4, 5 vs 3, 6 vs 2, 7 vs 1, 8 vs 11, 9 vs 10.

Night 5: 12 vs 5, 6 vs 4, 7 vs 3, 8 vs 2, 9 vs 1, 10 vs 11.

Night 6: 12 vs 6, 7 vs 5, 8 vs 4, 9 vs 3, 10 vs 2, 11 vs 1.

Night 7: 12 vs 7, 8 vs 6, 9 vs 5, 10 vs 4, 11 vs 3, 1 vs 2.

Night 8: 12 vs 8, 9 vs 7, 10 vs 6, 11 vs 5, 1 vs 4, 2 vs 3.

Night 9: 12 vs 9, 10 vs 8, 11 vs 7, 1 vs 6, 2 vs 5, 3 vs 4.

Night 10: 12 vs 10, 11 vs 9, 1 vs 8, 2 vs 7, 3 vs 6, 4 vs 5.

Night 11: 12 vs 11, 1 vs 10, 2 vs 9, 3 vs 8, 4 vs 7, 5 vs 6.

 Cheers,
Claude
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