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?

Either Ben won the race or not. This helps as two of the players say this happened.

If Ben did not win:

Both Ben and Cal made false statements, so one is the liar and the other is the knave and Abe is the knight.

That means Cal won the race, but Abe would have won if Cal had not interfered.

That means Ben is the knave and Cal is the liar.

If Ben won:

Both Ben and Cal made true statements, so one is the knight and the other is the knave and Abe is the liar.

Since Cal did not interfere with Abe, Ben is the knave and Cal is the knight.

Posted by Charlie on 2012-01-31 13:49:36