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Wimbledon

What is the maximum number of feasible entrants for the singles tournament at Wimbledon?

Each match eliminates one entrant and one entrant (the winner) remains uneliminated. Therefore, the maximum number of entrants is the maximum number of matches that could be played plus one.

Assume an entrant only plays once per day. How many matches on the final day?

Assume a maximum number of matches can be played on one day.

My estimate: 978 entrants (Since revised to 632; see later)

This answer is my estimate for the maximum number of matches that could be played plus one. Each match eliminates one entrant and one entrant (the winner) remains uneliminated.

Assumptions:

Only the singles tournament is played.

No player plays more than one match in a day.

Each match takes 90 minutes.

There are 20 courts.

There are 9 hours (540 mins) of daily playing time.

There is no rain!

Wimbledon lasts 14 days.

Assumptions 3, 4, 5 and 6 imply a maximum of 120 matches in a single day.

Each entrant only plays one match a day, we can therefore count backwards from finals day when only one match is played. We double the number of matches played each time, going back through the semi-finals, then the quarter-finals and so on.

Day 14: 1 (no. of possible matches on that day)

Day 13: 2

Day 12: 4

Day 11: 8

Day 10: 16

Day 9: 32

Day 8: 64

Day 7: 128!

It is not possible to play 128 matches on a single day, there is a maximum of 120. Therefore 120 matches can be played on that day and for the remaining 6 days.

Therefore, the maximum number of matches that can be played at Wimbledon =

1+2+4+8+16+32+64+(7*120)=967

Each match eliminates one entrant and one entrant (the winner) remains uneliminated.

Therefore, the maximum number of entrants to Wimbledon =

967+1=978

Revision

I have received several comments stating that 90 minutes is too short for the average match. This is certainly true at Wimbledon where they play the best of five sets. Looking at their official site the average number of sets played in the 2002 Championships was ~3.7. No average time was available, but lets say 40 minutes, which gives an average match length of 150 minutes or 2 ½ hours.

150 minutes per match gives a reduced maximum of 72 matches in a single day.

Therefore, the new maximum number of matches that can be played at Wimbledon =

1+2+4+8+16+32+64+(7*72)= 631

and the new maximum number of entrants to Wimbledon = 632

Note: This is not such a big reduction as might be expected with the large increase in match length. The final 7 days are unchanged as the limiting factor was not time, but the assumption that no player would play twice on the same day.

And the real answer?

632 is still well above the 128 entrants that actually do enter the Wimbledon fortnight but remember that it's not just singles that are played during the two weeks and that the question asked for a theoretical maximum.

There are clearly several "correct" answers to this question. If you have a different one (or a different question); e-mail it to WebMaster@IntellectualLoafing.com

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