While traveling with her pet tiger, Tatiana the Explorer wandered into the land of Pishta. Pishta was a land that followed the rules of knights, knaves and liars. While Tatiana was in the capital, the prince of Pishta, handsome and aristocratic, noticed her and asked her to marry him. The Queen however, did not want a commoner to marry her son, so she insisted that Tatiana prove herself by passing a test.

The night before the test the Prince confided to Tatiana, "You will be asked to choose between three doors. I will be behind the door furthest to the right. Your tiger and a wardrobe of peasant clothes will be in the other rooms. But be aware that if you choose the door that hides your tiger, your days of exploring will be over. If you choose the peasant clothes you will be forced to work in the castle. Remember my words my dear, for I love you and I promise to make you happy always."

The morning of the test the Queen led Tatiana to a hall with three doors. The Queen said, “For your test, you are to pick one of these three doors. One of these doors hides a fantastic wardrobe of new clothes for you. Behind another is where my son, the Prince, awaits. The third hides a ferocious man-eating animal. To help you make your decision, I have provided six counselors. Listen to what they say, because they have all been verified to be Knights. The selection of counselors was easy to make because, after all, there are no Liars in Pishta."

Tatiana listened to each of the six counselors:
Counselor A: The prince is not behind the left door. The animal is not in the library.
Counselor B: The wardrobe is not in the library. The animal is not in the kitchen.
Counselor C: The animal is not behind the right door. The prince is not behind the middle door.
Counselor D: The animal is to the right of the library. The prince is to the left of the library.
Counselor E: The wardrobe is behind the door to the left. The door to the left leads to the dining room.
Counselor F: The prince is not behind the right door. The right door does not lead to the kitchen.

Which door should Tatiana choose?

If this is correct, this is a fantastic puzzle!

Both the Prince and the Queen are Knaves.  Examining their statements:

Prince
------
TRUE "You will be asked to choose between three doors."
FALSE "I will be behind the door furthest to the right."
TRUE "Your tiger and a wardrobe of peasant clothes will be in the other rooms."
FALSE "But be aware that if you choose the door that hides your tiger, your days of exploring will be over."
TRUE "If you choose the peasant clothes you will be forced to work in the castle."
FALSE "Remember my words my dear, for I love you and I promise to make you happy always."

Queen
-----
TRUE "For your test, you are to pick one of these three doors."
FALSE "One of these doors hides a fantastic wardrobe of new clothes for you."
TRUE "Behind another is where my son, the Prince, awaits."
FALSE "The third hides a ferocious man-eating animal."
TRUE "To help you make your decision, I have provided six counselors."
FALSE "Listen to what they say, because they have all been verified to be Knights."
TRUE "The selection of counselors was easy to make because, after all, there are no Liars in Pishta."

The Queen's last statement, that there are no Liars in Pishta, is true.  Of the 36 combinations of rooms and doors, only ONE of them exists where none of the 6 counselors would be liars:

Left Door: Dining Room, Tiger
Middle Door: Kitchen, Prince
Right Door: Library, Wardrobe

This makes counselors A and F Knights, and B, C, D and E Knaves.  Any other possible combination makes at least one of the six counselors a Liar.

The puzzle gives the assumption that you are looking for the door with the Prince, but this is not the case.  By his own statements, he lied about the door he would be hidden behind, and he lied when he said he would love her.  He also lied when he said that if she chose the door with her pet tiger, her days of exploring would be over.

Therefore, Tatiana should pick the door of the LEFT, take her pet tiger, and continue on her way!  :)

Posted by tomarken on 2006-04-10 12:09:03