In every group of shepherds in a certain island, at least one is a knight, who always speaks truthfully, and at least one is a liar, who always speaks falsely.

A visitor approached four shepherds (denoted by A, B, C and D) on a hillside and asked each how many of the four were knights. These answers were given:

A: Three of us are knights.
B: One of us is a knight.
C: Two of us are knights.
D: None of us is a knight.

The visitor approached four more shepherds on another hillside (denoted by E, F, G and H) and asked how many were liars. Their answers follow:

E: We are all liars.
F: One of us is a liar.
G: Three of us are liars.
Shepherd H declined to speak.

How many of the shepherds on each of the two hillsides were knights?

Obviously, only one of A, B, C, and D can be a knight. Since there is at least one knight, there is exactly one knight out of A, B, C, and D. B said that there was one knight, so the knight is B.

Posted by Math Man on 2012-07-12 11:47:59