perplexus.info :: Numbers : The Tennis Tournament

The Tennis Tournament (Posted on 2002-06-13)

Another problem from the CBC website, this one submitted by Prof. Peter Rosenthal of the Mathematics Department of the University of Toronto:

This is a question about a tennis tournament. It's organized so that in each round players are randomly paired. If there is an odd number of players, the extra player sits out the round. Losers are all eliminated from the tournament. The rounds continue in the same way until there is only one person remaining, who becomes the champion. The question is: If there are X people who enter the tournament, how many matches will be played in the tournament?

Submitted by TomM

Rating: 2.1429 (7 votes)

Solution: (Hide)

I asked a question about organizing a tennis tournament. In each round entrants are randomly paired, if one is left over, she sits out a round. Each loser is eliminated from the tournament.
The process goes on until the final, and someone wins the championship. How can you know, given the number of entrants, how many matches will be played? You might have tried to do this in a complicated way, by counting and dividing, over and over.
Here's a better approach. Each match has a loser, and everyone except the champion loses exactly one match. So the number of matches is equal to the number of matches lost, which is the number of entrants minus 1 for the champion.
If there are X entrants, then there have to be x-1 losers, and x-1 matches.

Comments: ( You must be logged in to post comments.)

Subject	Author	Date
Puzzle Answer	K Sengupta	2023-09-06 09:40:30
Is this a joke?	Erik	2006-05-21 08:25:17
easy peasy	gohshj	2004-04-27 06:53:59
an easy one	mark hartman	2003-05-28 18:18:07
Simple	Tim Axoy	2003-03-30 11:28:01
Solution	friedlinguini	2002-06-13 02:53:29

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