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?

(1) All six are Liars. The race ended in a dead heat - a six-way tie. (Just kidding...But this puzzle would have been so much improved if that WERE the answer. Somehow make it so that every possible finishing order leads to a contradiction, so that only those imaginative enough to picture a 6-way tie would solve it. But as it is, solving this puzzle just involves mechanically eliminating the possibilities. It comes by its 2.6 rating honestly.)

(2) Assuming ties are not possible, they finished A-F-D-C-B-E. A is a Knave and all the others are liars. There are no Knights, Silver or otherwise.

Explanation:
They can't all be Knights, since they disagree. Since someone is telling the truth about the first place finisher, they can't all be Liars. There is at least one Knave.

As usual, we solve this problem by ignoring the boring Liars and the equally boring Knights, and concentrate on the interesting Knaves.

There are only 24 possible ways they could have finished, 4 each gotten by assuming that each of the 6 is a Knave. Of these, only one is possible, given the constraints of the puzzle. So the answer is: They finished A-F-D-C-B-E. A is a Knave and all the others are liars.

Here are the other 23 possibilities:

If A-E-D-F-B-C, then C told 3 consecutive lies and then the truth.

If B-C-A-E-D-F, then B told the truth and then consecutive lies.

If D-C-B-E-A-F, then B told the truth followed by consecutive lies.

If B-A-F-D-C-E, then D told consecutive lies and then the truth.

If B-E-F-A-C-D, then D told a lie followed by consecutive truths.

If C-D-B-E-F-A, then A told consecutive lies and then the truth.

If F-D-C-E-B-A, then A told consecutive lies and then the truth.

If C-B-E-D-A-F, then A told consecutive lies followed by the truth.

If C-F-E-B-A-D. then D told consecutive lies followed by the truth.

If A-D-C-F-E-B, then A told the truth and then consecutive lies.

If E-D-A-F-C-B, then B told a lie, the truth, and then consecutive lies.

If D-C-F-E-A-B, then A told a lie, the truth, a lie, the truth, and two consecutive lies.

If D-B-F-C-A-E, then B two lies and then the truth.

If A-E-D-B-F-C, then A told the truth, a lie, the truth, and then consecutive lies.

If F-E-A-B-D-C, then E told two lies and then the truth.

If E-C-A-B-F-D, then A told a lie, the truth, and then consecutive lies.

If E-D-A-C-F-B, then B told a lie, the truth, and then consecutive lies. If F-B-E-D-A-C, then C told two lies and then the truth.

If A-B-F-D-E-C, then A told the truth and then consecutive lies.

If F-D-B-C-E-A, then B told a lie, the truth, and then consecutive lies.

If F-A-B-D-E-C, then D told consecutive lies, then the truth.

If E-C-F-A-B-D, then A told a lie, the truth and then consecutive lies.

If B-C-E-A-F-D, then A told a lie, the truth, and then consecutive lies.





Edited on December 16, 2003, 12:53 am

Posted by Penny on 2003-12-15 20:46:54