Wednesday, March 31, 2010

Knights and Knaves

On a magical island of knights and knaves (from chapter 1) there are 2 kinds of people: knights, who must always tell the truth, and knaves that must always lie.

There is a cruel 3-d reality televison show:Your Money or Your Life, in which there are two doors to choose from. Behind one door, lay untold riches, behind the other door, certain doom! One door is guarded by a knight, the other by a knave. You may ask one guard a yes/no question before opening the door of your choosing. What question should you ask?

You don't know which door has the treasure, and you can't tell a knight from a knave based upon appearance.

(again teaser question from chapter 1)

If you were to ask:

"Is the treasure behind the door at yon guard-post my good gentleman?"

(Must speak with a noble tongue)

If the guard were the knight, and the treasure is behind the door, he would say yes.
however, if the guard were the knave, and the treasure is still behind the door, then he would say no. If you followed the knave's advice then you would pick the door of doom.

Knight AND treasure, answer = Yes
Knight And Not treasure answer = No

Knave And treasure, answer = No
Knave And Not Treasure, answer = Yes.

This doesn't help, since half of the time the answer is yes and half no. This is no better than guessing.

After some deliberation, it seems that you should ask either guard this question: "Yon Noblest of Guards, which door would your fine compatriot pick to select the treasures?"

Guard = knight then he would have to tell the truth, so he'd pick the door of doom. this is the door that the Knave would choose as the treasure door. Remember the Knave isn't out to get you, he just can't tell the truth.

Guard = knave, then he'd lie about the door that the knight would select, so he would also pick the door of doom as the treasure door.

So the best thing to do would be to ask the above question and select the door that isn't recommended as the treasure door by the the guard.

With this strategy, you should have a lifetime of fortune and good luck, and a certain victory!

No comments:

Post a Comment