PK 2016 Q11
11. A tennis tournament was played on a knock-out basis. The following list is of all but one of the last seven matches (the quarter-finals, the semi-finals and the final), although not correctly ordered: Bella beat Ann; Celine beat Donna; Gina beat Holly; Gina beat Celine; Celine beat Bella; and Emma beat Farah. Which result is missing?
- A Gina beat Bella
- B Celine beat Ann
- C Emma beat Celine
- D Bella beat Holly
- E Gina beat Emma
Pink Kangaroo 2016, Question 11. © UK Mathematics Trust. Original paper on ukmt.org.uk
Answer: E Gina beat Emma
The most matches that any player could play is three. Any player who wins twice will play in the final. Hence Celine and Gina must be the two finalists, and Gina beat Celine. This means Gina must have won three matches altogether, but only two are recorded. Hence the missing result must be that Gina beat someone.
All the other players must have lost once, but Emma has no loss recorded, so the missing result must be that Gina beat Emma.
Indeed, from the given information we can deduce that the pairings must have been as shown (using players' initials instead of their full names):
Solution © UK Mathematics Trust, from the PK 2016 solutions.