KMCG

He Cannot Lie

Wednesday, June 22, 2016 A.D.

Welcome to the Island of Knights, Knaves, and Sir Mix-a-lot! There are a few things you should know about this island:

  • Knights always tell the truth
  • Knaves always lie
  • There is exactly one knight named “Sir Mix-a-lot”. Like every other knight, he cannot lie.

You run into three inhabitants on the island. Earlier in the day, a friend of yours (a knight, so we know his statements to be true) told you that one of these three is Sir Mix-a-lot. They make the following statements to you:

A: At least one of the three of us is a knave
B: C is a knight.

Keeping in mind that there is exactly one knight named Sir Mix-a-lot, which one of the three is he?

 

The Solution:

First, we need to figure out what A is. Let's say he is a knave and is therefore lying. That would make his statement about at least one of them being a knave true, so we have a contradiction. It's impossible for A to be a knave in this case, so he must be a knight. That means that either B or C (or possibly both) has to be a knave.

With that in mind, let's look at B's statement. He claims that C is a knight. If that's true, then that makes B a knight as well for making a true statement. We know that can't be the case, however, since we know from A that at least one of them is a knave. B's statement has to be false, because if it were true it would be a contradiction. We now know B to be a knave and the statement he made to be false. Therefore B and C are both knaves, and A is the knight named Sir Mix-a-lot.

For more knights and knaves, get some of Raymond Smullyan's puzzle books. I tend to like his older books, but that's just me.