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?

Looking at the previous solutions I pretty much used the same logic as FatBoy, SK and Charlie to work out the basics. ie.

1. There are no knights
2. There is one (and only one) knave of the form TFTFTF, which must be A, E or F
3. There are no knaves of the form FTFTFT

But then I used a different (and simpler, therefore superior!!! ;-) ) approach to get the rest of the answer...

The above 3 basic statements mean that everybody lied about who came last - therefore by elimination E must have come last. Which means that neither E nor F can be the knave (since E appears in truth telling positions for both E & F). Thus A must be the knave.

So at this point we have A ? D ? B E

We also know that everybody lied about who came 4th - therefore by elimination C must have come 4th and F finished 2nd.

So the order is AFDCBE

I can't wait to see what wonderful insight Dr Math can bring to the discussion. I'd have a look myself, but I'm not bright enough to use the search function.

Posted by fwaff on 2003-12-15 10:50:51