23 Oct 2013

A Chess Tournament: Middle Secondary Mathematics Competition Question

A speed chess tournament is organised according to the following rules. Each round consists of all one-game matches played between two players. A player is eliminated from the tournament once that player has lost 2 games. No games are drawn. The draw for each round is done by randomly drawing names from those players still in the tournament. If there are an odd number of players in a round, a bye* is given to one player randomly drawn from the set of players with the smallest number of losses and the least number of byes already received; this takes place before the draw for that round.

Given that 33 players start the tournament, what is the minimum number of games needed to guarantee reaching one outright winner?

*Note that a bye means the player does not play in that round but still passes onto the next round.

Feel free to comment, ask questions and even check your answer in the comments box below powered by  Disqus Google+.


This space is here to avoid seeing the answers before trying the problem!


If you enjoy using this website then please consider making a donation - every little helps :-)

You can receive these questions directly to your email box or read them in an RSS reader. Subscribe using the links on the right.

Don’t forget to follow Gifted Mathematics on Google+Facebook or Twitter. You may add your own interesting questions on our Google+ Community and Facebook..

You can also subscribe to our Bookmarks on StumbleUpon and Pinterest. Many resources never make it onto the pages of Gifted Mathematics but are stored in these bookmarking websites to share with you.

No comments:

Post a Comment

Related Posts Plugin for WordPress, Blogger...