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Tournaments with a twist

by diana.hole
Tags: combination, twt
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Apr2-12, 04:44 AM
P: 8
1. The problem statement, all variables and given/known data
The Bunalong Tennis Club is running a mixed doubles tournament for families from the district. Families enter one female and one male into the tournament. When the tournament is arranged, the payers discover the twist; they never partner or play against their own family member.

The tournament, called a TWT, is arranged so that;

1. each player plays against every person of the opposite gender, except for his or her family member, exactly once.

2. Each player plays against every person of the same gender exactly once

3. Each player partners every person of the opposite gender, except for his or her family member, exactly once.

Using the notation M1 and F1 for the male and female for family 1, M2 and F2 for family 2, and so on. An example of an allowable match is M1 F3 v.s. M6 F4.

find all TWTs for four families

2. Relevant equations

3. The attempt at a solution
i already have one TWT thus far;
M1F4 vs M2F3
M3F2 vs M4F1
M1F3 vs M4F2
M2F4 vs M3F1
M1F2 vs M3F4
M2F1 vs M4F3
I'm not quite sure what to do now, and whether all of the other TWTS will basically just be rearrangements of this one, since they all play each other once, partner each other once etc, or whether they'll play different people with different partners, yet still satisfying the rules.
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