You are on the island of Knights and Liars exploring an ancient monastery. The old, worn guidebook that the abbot loaned has helped you navigate the catacombs and find all of the interesting old crypts. You are heading back out to garden, still following your guidebook, when you come to a pair of ornately carved doors.
The guidebook describes the two doors: "At this point there are two doors. One will return you to the garden. You must be careful not to open the other door, because beyond it is a sheer drop into the cesspit. The ladder that the monks used to access the chamber was removed when the new wing of the abbey was built with modern plumbing.. Carved on each door in the ancient language is its destination. The door to the garden is marked...."
At this point, the page is torn. You think to yourself, "maybe, if I'm very careful...." but when you look at the doors, you see that the way they are constructed, you cannot open a door without stepping through.
You are about to despair when you hear approaching footsteps. Someone is coming! A monk comes into view. He is wearing a red sash and carrying a basket of food. You remember the ceremony you watched this morning., and realize that he is headed for a meditation chamber deep in the catacombs and will remain there for three days. So much for just following him out.
You remember that the Abbot (a Knight) told you that during the time of their purification, monks are under a vow of near silence. They areallowed to speak only one word per day, in answer to a yes-or-no question. But they must speak it in the ancient language. You remember that "Zim" is one of the words, but you don't remember whether it is "yes" or "no." (Although you can't remember it, the other word is "Dahl.")
Can you ask one question and learn which door to take without knowing either whether the monk is a Knight or a Liar, or whether "zim" means "yes" or "no"?
This puzzle is, I believe, original to me. It was influenced by the books of Raymond Smullyan, which I haven't read in many years. If this should prove to be a re-working of one of his puzzles, I apologize.
I would point to a door at random and ask the monk:
"If I asked you 'does this door lead to the garden?', would you say Zim?"
There are eight options:
- Zim means "yes", the Monk is a "liar", the Door "isn't" the exit:
If I asked the monk "is this the exit?" he would answer Zim (yes), lying. So, in answer to my actual question, he would say DAHL (no), denying this fact.
- Zim means "yes", the Monk is a "liar", the Door "is" the exit:
If I asked the monk "is this the exit?" he would answer Dahl (no), lying. So, in answer to my actual question, he would say ZIM (yes), denying this fact.
- Zim means "yes", the Monk is a "knight", the Door "isn't" the exit:
If I asked the monk "is this the exit?" he would answer Dahl (no). So, in answer to my actual question, he would also say DAHL (no).
- Zim means "yes", the Monk is a "knight", the Door "is" the exit:
If I asked the monk "is this the exit?" he would answer Zim (yes). So, in answer to my actual question, he would also say ZIM (yes).
- Zim means "no", the Monk is a "liar", the Door "isn't" the exit:
If I asked the monk "is this the exit?" he would answer Dahl (yes), lying. So, in answer to my actual question, he would say DAHL (yes), denying this fact.
- Zim means "no", the Monk is a "liar", the Door "is" the exit:
If I asked the monk "is this the exit?" he would answer Zim (no), lying. So, in answer to my actual question, he would say ZIM (no), denying this fact.
- Zim means "no", the Monk is a "knight", the Door "isn't" the exit:
If I asked the monk "is this the exit?" he would answer Zim (no).
Solution (I think)
