Game, set, match – Wimbledon Math
Wimbledon! This great tennis tournament started on June 22. This year, 128 women and 128 men will battle it out for the women’s and men’s singles titles over a two week period.
“In each round of the singles events the players are paired off, and the winners of these matches proceed onto the next round. The final round, consisting of a single match, decides the title. How many matches will the champion play? How many matches are played in the whole event?
What if there were 1024 players in each event? What can you say about an event with 2n players?
Solution
In each of the Wimbledon singles events, the rounds are as follows:
- Round 1: 128 players playing 128/2 = 64 matches;
- Round 2: 64 players playing 64/2 = 32 matches;
- Round 3: 32 players playing 32/2 = 16 matches;
- Round 4: 16 players playing 16/2 = 8 matches;
- Round 5 (quarterfinal) : 8 players playing 8/2 = 4 matches;
- Round 6 (semifinal): 4 players playing 4/2 = 2 matches;
- Round 7 (final): 2 players playing 2/2 = 1 matches;
Therefore the men’s and women’s champions each play 7 matches, one for each round. And in total there were
But what about an event with 2n players? From our arguments above, the champion would play n matches to win the title, and a total of 2n-1 matches would be played during the event.” Article from Plus.Maths.org