Math Challenge Problem

The Math Challenge problem has returned to UNC's School of Mathematical Sciences! This is a problem that everyone is welcomed to try their hand at. New problems monthly.  

March Challenge

The Dance of the Knights and Knaves

Deep in the forest of the knights and knaves, you stumble on a peculiar sight: a large group of trolls is dancing in a circle. Every once in a while, all the trolls stop, each facing either clockwise or counterclockwise around the circle. They all point to the troll standing in front of them (who might or might not be facing them) and shout, "you are a knave!" Then every troll turns around, points to that troll, and shouts, "you are a knight!"

Of course, even in this bizarre ritual, knights always tell the truth and knaves always lie.

The Challenge: Assuming all dancing trolls are either knights or knaves, how many trolls could be dancing?  Which numbers of trolls are possible, and which are impossible?

challenge art

Submit solutions to Ross 2239G or by email to oscar.levin@unco.edu.
Deadline: Friday, March 31.

Win PRIZES! A winner will be selected from all correct answers received for each challenge problem to receive a fun math prize of his or her choice.

 

Previous Problems

2016-2017

September Challenge | October Challenge | November Challenge | January Challenge | February Challenge

2015-2016

September Challenge 1 | September Challenge 2 | October Challenge 1 | October Challenge 2 | November Challenge 1 | November Challenge 2 | January Challenge | February Challenge 1 | February Challenge 2 | March Challenge 1 | March Challenge 2 | April Challenge

2014-2015

September Challenge 1 | September Challenge 2 | October Challenge 1 | January Challenge | February Challenge 1 | February Challenge 2 | March Challenge 1 | March Challenge 2 | April Challenge 1 | April Challenge 2

2013-2014

September Challenge 1 | September Challenge 2 | October Challenge 1 | October Challenge 2 | November Challenge 1 | November Challenge 2 | January Challenge | February Challenge 1 | February Challenge 2 | March Challenge 1 | March Challenge 2 | April Challenge 1 | April Challenge 2

2012 - 2013

September Challenge | October ChallengeNovember Challenge | January Challenge | February Challenge  | March Challenge  | April Challenge

2011 - 2012

September Challenge | October Challenge | November Challenge | January Challenge | February Challenge 1 | February Challenge 2 | March Challenge | April Challenge