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by Demetrius Nunes

In a single-elimination tournament, there is usually a previously established
ranking for the participating players or teams, such as that the best players or
teams are matched against the worst ones. This is done this way so there is a
higher chance for the top players/teams to meet in the final.

For example, in a small 8-player tournament, there would be 3 rounds. This first
round would be setup like this:

	Round 1
	1 x 8
	2 x 7
	3 x 6
	4 x 5

This is easy enough. The tough part is arranging the pairing for the following
rounds respecting the best vs worst rule, so, imagining that all the favorites
won their games, we would have 1x4 and 2x3 in round 2 and then finally 1x2 in
the final. For this to happen, the tournament would have to be arranged this
way:

	R1  R2  R3
	============
	1
	---
	   |---
	---    |
	8      |
	       |---
	4      |   |
	---    |   |
	   |---    |
	---        |
	5          |
	           |----
	2          |
	---        |
	   |---    |
	---    |   |
	7      |   |
	       |---
	3      |
	---    |
	   |---
	---
	6

If the numbers of players/teams is not a potency of 2, then the top players
would have a "bye" in the first round, so, a 6-player draw would go like this:

	R1  R2  R3
	============
	1
	---
	   |---
	---    |
	bye    |
	       |---
	4      |   |
	---    |   |
	   |---    |
	---        |
	5          |
	           |----
	2          |
	---        |
	   |---    |
	---    |   |
	bye    |   |
	       |---
	3      |
	---    |
	   |---
	---
	6

So, this quiz is about writing a single-elimination tournament generator for any
number of players/teams obeying the best vs worst rule in all rounds.

For a quick look at correct answers see this "got-the-job-done" javascript/html
implementation at:

	http://www.crowsdarts.com/brackets/playoff-chart.html

We are looking for correct data modeling and calculation, not for correct
presentation output of the tournament draw, but it would be nice to implement a
#to_s output like the ones seen above (or even better: how about a beautiful
RMagick generated image?!). In all cases, keep the model and presentation
cleanly separated.