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### Darts Tournament with Eight Players

```Date: 10/05/2002 at 22:53:46
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

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/
```
Associated Topics:
High School Permutations and Combinations

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