Darts Tournament with Eight PlayersDate: 10/05/2002 at 22:53:46 From: Chad Lakin Subject: Story problem There are eight players in a darts tournament. Each player plays one game against each of the other players. How many dart games will be played in the tournament? Find a pattern to determine the number of games played no matter how many players there are. The number is 28 but I don't know how to get the mathamaticical formula. Date: 10/06/2002 at 11:05:50 From: Doctor Ian Subject: Re: Story problem Hi Chad, Let's look at a simpler tournament, in which there are only three players: Pat, Chris, and Jody. Suppose we're going to set up a match at random, by choosing a pair of competitors. How many ways can we choose the first competitor? There are three possible choices, right? 1. Pat and _____ 2. Chris and ____ 3. Jody and ____ Now, in how many ways can we choose the second competitor? We have only 2 choices. Pat and _____ -> 1.1. Pat and Chris 1.2. Pat and Jody Chris and ____ -> 2.1. Chris and Pat 2.2. Chris and Jody Jody and ____ -> 3.1. Jody and Pat 3.2. Jody and Chris So the number of pairings we could have is 3*2, or 6: But wait! Choosing Pat and Chris is the same thing as choosing Chris and Pat, right? So there are _really_ only half as many choices as we thought: (3*2)/2, or 3. Can you use the same logic to come up with 28 pairings for 8 players? - Doctor Ian, The Math Forum http://mathforum.org/dr.math/ |
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