Three friends, Alan, Bob and Cecil, sit down at a park bench. Each of them is a Knight or Liar and each knows what the other two are.

Forgetful Bob, well known for his flamboyant hats that are either red, white or blue, asks Alan: "What colour hat am I wearing today?"

Alan replies: "There is a chance Cecil would tell you it's blue. If you saw it, there is a chance you would say it is white."

Bob sighs, "I should have asked Cecil - he always tells me the truth..."

What colour hat is Bob wearing?

Bob's hat is red.

From bob's statement:
If bob is a knight, then cecil is too. If bob is a Liar, then cecil is a Liar also.

If Bob and Cecil are both Knights, then Alan must be a liar. (He says they'll give different answers). From this, the hat must be red.

If Bob and Cecil are both Liars, then Alan must be a Knight. (He's saying at least one of them will be lying. Thus both are liars). Thus the hat is red.

Either way, the hat is red.

Posted by Happy on 2002-06-13 13:11:08