Question

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.

Answer 1

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

Answer 2

A) Explain why there cannot be fewer than four families in a TWT
B) Give an example of a TWT for four families in which one of the matches is M1F4 v M2F3
C) Give an example of a TWT for five families in which one of the matches is M1F3 v M2F5.
d) find all the TWTs for four families

Answer 3

Stop trying to cheat on the Mathematics Challenge for Young Australians.