Making Maths Count
Maths Week Scotland 2019 – Mixed Doubles
Problem 7: Mixed Doubles
Eight keen tennis players played a mini mixed-doubles tournament one Saturday afternoon and then went on to a dance in the evening. They are Andy, Clarissa, Emma, Gordon, Jan, Liz, Sunita and Zak. At one point during the evening:
- Emma was dancing with Zak
- Liz was dancing with Clarissa’s tennis partner
- Sunita was dancing with Liz’s tennis partner
- Andy was dancing with Gordon’s tennis partner
- Gordon was dancing with Zak’s tennis partner
Identify the pairs of tennis partners.
Solutions to Problem 7:
Answer The pairs of doubles partners were:
Zak and Sunita, Gordon and Liz, Andy and Clarissa, Jan and Emma.
Since Emma was dancing with Zak, by the next two statements, Zak cannot be Clarissa’s tennis partner (as Liz was dancing with him) and also cannot be Liz’s partner (as Sunita was dancing with him). Zak cannot be Emma’s partner, since by the last statement Gordon was dancing with Zak’s partner. So Zak was partnered by Sunita.
As Gordon was dancing with Sunita, by the third statement, Gordon was Liz’s partner.
So Andy was dancing with Liz and by the second statement Andy and Clarissa were partners.
That means that the final doubles partnership was Jan and Emma.