Quiz question
Can you work out how many quizzes have to be played before we have a winner?
Age
11 to 14
Challenge level
Problem
There are 81 players taking part in a knock-out quiz tournament.
Each match in the tournament involves three players, and only the winner remains in the tournament.
How many matches are required until there is an overall winner?
This problem is taken from the UKMT Mathematical Challenges.
Student Solutions
Answer: 40
Counting in rounds
81 players
First round: 81$\div$3 = 27 matches, with 27 winners
27 players
Second round: 27$\div$3 = 9 matches, with 9 winners
9 players
Third round: 9$\div$3 = 3 matches, with 3 winners
3 players
Fourth round: 1 final match
1 player - winner
Total: 27 + 9 + 3 + 1 = 40 matches
Counting the losers
After each match 2 players are knocked out.
At the end of the tournament 80 players will have been knocked out (at a rate of 2 players per match).
This means that we will need 40 matches altogether.