Another Race (Posted on 2003-12-15)

	Submitted by Gamer
Rating: 3.3636 (11 votes)
Solution:	(Hide)
First of all, every other statement someone makes is logically equivalent. Also, since Knights, Knaves, and Liars are never mentioned by anyone, you can break the 6 groups of 6 statements into 12 logically equivalent statmenets: About the 1, 3, 5 positions in the race: 1: A B C D E F 3: D F E F A B 5: B C A A F F About the 2, 4, 6 positions in the race: 2: C D D E B C 4: E E F B D A 6: F A B C C D If two people say the same thing, it means everything else they say is logically equivalent. For example, C and D both said that A came in fifth place, but differed in opinion about who came in first and third place. Since both of them couldn't have come in first place, anything in the same column with the A in fifth place (1: C D, 3:E F, 5: A A, in this example) is eliminated. When this is applied to all of them, the following grid can be constructed: _A_B_C_D_E_F 1|? X X X X ? 2|? X X X X ? 3|X ? X ? X X 4|X X O X X X 5|X ? X ? X X 6|X X X X O X F thinks E was in fifth place. Since E is in sixth place, his statements about first and third place must be wrong as well. _A_B_C_D_E_F 1|O X X X X X 2|X X X X X O 3|X X X O X X 4|X X O X X X 5|X O X X X X 6|X X X X O X Filling in the only remaining choices gives the solution grid. So the order is A F D C B E; A is a knave and the others are liars.

	Subject	Author	Date
	Problem Solution	K Sengupta	2007-05-04 12:40:07
	dddd	paul	2004-03-04 22:23:44
	Two independent solutions (No computer assistance)	Penny	2003-12-15 20:46:54
	No Subject	krdmt5_000	2003-12-15 15:57:56
	Another solution	fwaff	2003-12-15 10:50:51
	... and the computer way.	Charlie	2003-12-15 09:28:25
	solution	Charlie	2003-12-15 09:22:05
	Full Solution	SilverKnight	2003-12-15 09:19:54
	First Thoughts	FatBoy	2003-12-15 08:55:22