KMCG

The Fullest House of All, Part I

Saturday, July 30, 2016 A.D.

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

  • Knights always tell the truth
  • Knaves always lie

Did you know that Mary-Kate and Ashley Olsen are residents on the Island of Knights and Knaves? They are! For the sake of this blog post!

There's a problem, though. It's widely known that one of the sisters is a knave and the other one is a knight, but since there's no way to tell them apart you never know if you're hearing the truth or a lie from one of them.

One day you run into one of the twins at Burlington Coat Factory. You see your chance to find out which one is the knight and which one is the knave once and for all, but time is limited. What's the shortest single question you could ask to find out?

Solution

You could ask "Are you Mary-Kate?" If you get a "No" response and you are talking to Mary-Kate, then she is a knave and Ashley is the knight. If you get a "No" response and you're really talking to Ashley, then Ashley is truthful and a knight, and Mary-Kate is still a knave. In summary, if you get a "No" response, Ashley is the knight no matter what. The reverse holds true if you get a "Yes". In that case, Mary-Kate is the knight and Ashley is the knave no matter what.