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?

Not that hard i guess?

1st case: A-liar B-knight

By B, C-knight. By A, the hat is red.

2nd case: A-liar B-liar

By B, C-liar. By A, hat is blue and white, contradiction.

3rd case: A-knight B-liar

By B, C-liar. By A, not blue, not white, the hat is red.

since only case 1 and 3 are valid and they lead to the same conclusion, Bob's hat is red.

Posted by Terence on 2005-10-13 15:27:03