How Can a Mixed Doubles Tournament Avoid Family Pairings?

  • Thread starter diana.hole
  • Start date
In summary, the Bunalong Tennis Club is holding a mixed doubles tournament for families in which one male and one female member from each family compete against other families. The tournament has the following rules: each player will play against every person of the opposite gender, except for their own family member, exactly once; each player will also play against every person of the same gender once; and each player will partner with every person of the opposite gender, except for their own family member, exactly once. An example of an allowable match is M1F3 vs M6F4. There is already one TWT with the pairs M1F4 vs M2F3, M3F2 vs M4F1, M1F3
  • #1
diana.hole
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Homework Statement


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


Homework Equations


N/A


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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  • #2
Consider the match in which M1 partners F2. Who are the possible opposing pairs?
Having chosen that opposing pair, is the rest of the tournament determined?
 

1. What is a "Tournament with a twist"?

A "Tournament with a twist" is a unique and unconventional type of tournament that introduces unexpected rules or challenges to traditional tournament formats. This twist adds a level of excitement and unpredictability to the competition.

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There are endless possibilities for adding twists to a tournament. Some common examples include changing the rules of the game, adding handicaps, introducing surprise challenges, or incorporating unconventional scoring methods.

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