When I went to the race track in Racing Town, a town made up only of Knights which always tell the truth, Knaves which tell truths and lies in an alternating pattern, and Liars which always lie, a race between 6 citizens of that town had just finished.

I went to the 6 citizens and asked each of them the order that all 6 finished. They all gave me different responses, each thinking themselves as winning, displayed here left to right as first to last.

A: A C D E B F
B: B D F E C A
C: C D E F A B
D: D E F B A C
E: E B A D F C
F: F C B A E D

From what they said, I was able to figure out what the correct order was. What is it?

Someone will probably solve this right away so I want to get my first thoughts so you folks won’t think I never contribute...

At least four of the six respondents must be liars. Here’s why. Since they all identify themselves as having been first there can be no more than one Knight.
If there is more than one Knave, their answers for every second questing would have to line up unless they were lying in different (ie one lies to the first third and fifth questions the other lies to the second fourth and sixth) no such matching pattern exists so there is either only one knave or two and one answered the first question truthfully which means there can not be a knight…

Posted by FatBoy on 2003-12-15 08:55:22