In a remote island, three people Abe, Ben and Cal took part in a running race. They belong to three different types: Knights, who always tell the truth; Liars who always lie and, Knaves who alternatively tell a truth or lie. It is known that precisely one of Abe, Ben and Cal is a knight, precisely one of them is a liar and the remaining is a knave. It is also known that there was precisely one person who reached the first position in the said race.

Following are some statements made by them:

Abe
1. I would have won the race if Cal had not come in my way to restrain me in the final part.
2. Cal won the race.

Ben
1. I won the race.
2. Cal came in Abe’s way, to restrain him from winning the race.

Cal
1. Ben won the race.
2. I did not come in Abe’s way, to restrain him from winning the race.

Find the types each of the three men belong to. Who won the race?

Abe could not have won the race, because each person claimed someone other than Abe won, meaning each would have told a lie.

If Ben won the race, then Ben and Cal would each have made a true statement about the winner, making Abe the Liar.  This would make Ben the Knave and Cal the Knight.

If Cal won the race, then Abe must be the Knight.  This would make Ben the Knave and Cal the Liar.  Either way, Ben is definitely the Knave.

Examining the claim that Cal restrained Abe in the final part, if this did indeed occur, it is unlikely that either Cal or Abe won the race, making Ben the winner.  But both of these statements cannot be true since Ben the Knave made both claims.  If Ben's second claim is true, then in all likelihood his first statement would also be true.  Thus, his second statement cannot be true, making his first statement true.


Therefore:

Abe = Liar
Ben = Knave & Winner
Cal = Knight

Winner = Ben

Edited on February 3, 2012, 12:24 am

Posted by hoodat on 2012-02-02 07:54:45