# Tournaments with a Twist (maths problem solving) The Bunalong Tennis Club is running a mixed doubles tournament for families from the district. Families enter one female and one male into the...

Tournaments with a Twist (maths problem solving)

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.

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### 8 Answers

thats ironic coming from someone with the name of a question in the booklet

but u searched for it u can't talk mate

Although it is possible for the Male vs Female and Male vs Male and Female vs Female but it is not possible for the doubles/mixed, meaning that the only possible matches for the doubless are :

M1F3 vs M2F4

M1F4 vs M2F3

M2F1 vs M3F4

M2F3 vs M4F1

M2F4 vs M3F1

M3F1 vs M4F2

M3F2 vs M4F1

Therefore in total there should be 7 matches for the doubles.

najm1947, that doesn't work because the players would be playing against their own family.

The possible TWTs for four families are as under:

**1. Male vs Female:**

(M1,F2), (M1,F3),(M1,F4),(M2,F1),(M2,F3),(M2,F4),(M3,F1), (M3,F2),(M3,F4),(M4,F1),(M4,F2),(M4,F3) - **Total: 12 Matches**

**2.a Male vs Male:**

(M1,M2), (M1,M3),(M1,M4),(M2,M3),(M2,M4),(M3,F4) - **Total: 6 Matches**

** 2.b Female vs Female:**

(F1,F2), (F1,F3),(F1,F4),(F2,F3),(F2,F4),(F3,F4) - **Total: 6 Matches**

**3. Mixed Doubles**

(M1F2,M2F1),(M1F2,M2F3),(M1F2,M2F4),

(M1F3,M2F1),(M1F3,M2F4),

(M1F4,M2F1),(M1F4,M2F3),

(M2F1,M3F2),(M2F1,M3F4),

(M2F3,M4F1),(M2F3,M4F2),

(M2F4,M3F1),(M2F4,M3F2),

(M3F1,M4F2),(M3F1,M4F3),

(M3F2,M4F1),(M3F2,M4F3),

(M3F4,M4F1),(M3F4,M4F2),(M3F4,M4F3) – **Total: 20 Matches**

YOU GUYS ARE CHEATING FOR THE MATHS COMPETITION, IM TRYING MY HARDEST TO COMPLETE IT BY MYSELF WHILE YOU GUYS ARE CHEATING!!!!

hi najm1947, could you please help me solve a smilair question:

Give an example of a TWT for five familes in which one of the matches is M1F3 vs M2F5!

It would be incredible if you could solve it as soon as possible.

Kind regards.