Exercise 29

 

Assessment started: undefined.

Item 1

You arrive at a fork in the road and need to choose the correct path that leads to your destination.

There are two people standing at the fork, and you know that one must be a knight and the other must be a knave.

A knight will always tell the truth whereas a knave will always lie.

What single question could you ask one of the people to determine the correct path, A$A$ or B$B$?

• Which is the correct path?
• What path would the other person tell me to choose?
Solution

If you ask the questions “Which is the correct path?”, “Shall I choose path A$A$” or “Shall I choose path B$B$” , then the knight and knave would give opposite answers. For example: If A$A$ is the correct path, the knight will tell you to choose A$A$ and the knave will tell you to choose B$B$. You won’t be able to make any deductions from the question asked.
But, if you ask the remaining question, the knave will say that the other person will tell you to select path B$B$ and the knight will tell the truth and say that the other person will tell you to choose path B$B$. Hence, you’ll get to know that the correct path is A$A$.