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?
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Submitted by Leming
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Rating: 4.5500 (20 votes)
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Solution:
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(Hide)
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Counselors A, C and F each claim the Prince in not behind a different one of the doors. These statements conflict with what the Queen said. So between Counselors A, C, F and the Queen someone has lied. The Queen told the truth in her first statement. Thus she is not a Liar and every odd statement she makes should be the truth. Her third statement says that the Prince is behind one of the doors, So, one of A, C, and F lied.
Now, the fact that any of the counselors lied conflicts with the Queen’s 6th statement. This means that the Queen lied and is thus a Knave. From the Queen’s 6th statement: not all of the counselors are Knights, and from her 7th statement, none of them are Liars.
Finding the Prince.
Assume the Prince is where he said – behind the door to the right.
Statement D2 is false. Since there are no Liars in Pishta D1 must be true, and the animal must be behind the middle door, the library is the left door which must be where the wardrobe is hidden. We also know that F1 is false, making F2 true and the middle door is the kitchen with the animal. These two combinations make B1 and B2 false, and making Counselor B a Liar. But since there are no Liars in Pishta, the Prince must have lied and he is not behind the right door.
Assume the Prince is behind the left door.
This makes E1 false and thus E2 true. The Prince is in the dining room. A1 is also false, forcing A2 to be true: The animal is not in the library, but is in the kitchen. This forces the wardrobe to be in the library. This makes both B1 and B2 false. Thus the Prince is not behind the left door.
Assume the Prince is behind the middle door.
This makes C2 false and forces C1 to be true. The animal is behind the left door, and the wardrobe is behind the right door. Then E1 is false and E2 is true. The animal is in the dining room on the left. Then D1 is false and D2 must be true. The library is behind the right door. This makes B1 false forcing B2 to be true – which it is. Finally, F1, F2, and A1, A2 are all true.
The Prince is behind the middle door.
However, the Prince lied at least once and must be a truth-first Knave. This makes his 2nd, 4th and 6th statements to be lies. He was not behind the right door – the wardrobe was. The Prince stated truthfully that the other two doors hid: a wardrobe of peasant clothes that if chosen would lead to forced labor in the castle; and Tatiana’s Tiger. He lied about loving her and making her happy and lied that if her Tiger was chosen she would never explore again.
Tatiana should choose the left door to the dining room, get her Tiger, make a sandwich and be on her way. |
