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?

(In reply to three solutions? by Dej Mar)

Solution 1 is not possible

If Ben is the Knight then Ben won the race and Cal obstructed Abe.
That means that Abe told the truth about being restrained by Cal and lied about Cal winning the race - making him the Knave.

That makes Cal the liar - yet he says that Ben won the race, which is true if Ben is the Knight.

A lot of (unnecessary) mathematical notation to get a relatively easy problem wrong.
Solutions 1 and 2 are both possible.

Posted by scott on 2013-04-12 12:56:00