Hosted by The Math Forum

Problem of the Week 980

Everyone's A Winner

_____________________________________________
MacPoW Home ||  Forum PoWs ||  Teachers' Place ||  Student Center ||  Search MacPoW
_____________________________________________

In a round-robin tournament, a player A is a gold medal winner provided, for every other player C, either A beat C or there is a player B so that A beat B and B beat C. Is it possible for a 10-player tournament to have ten gold medal winners?

Bonus Problem: Determine the set of n for which it is possible for an n-player tournament to have n gold medalists.

Source: The recent Konhauser Problemfest had an amusing problem on champions in a tournament. Here is a variation that seems equally amusing, pointed out by Richard Guy. It is in his recent MAA book with Paul Vaderlind and Loren Larson: "The Inquisitive Problem Solver" (section 250).
© Copyright 2003 Stan Wagon. Reproduced with permission.

[Privacy Policy] [Terms of Use]

_____________________________________
Home || The Math Library || Quick Reference || Search || Help 
_____________________________________

© 1994-2014 Drexel University. All rights reserved.
http://mathforum.org/
The Math Forum is a research and educational enterprise of the Drexel University School of Education.The Math Forum is a research and educational enterprise of the Drexel University School of Education.


4 March 2003