You are facing four doors, each of which leads either to gold or to a tiger. Any door leading to gold has a true statement on it; any door leading to a tiger has a false statement on it.

Assuming you want to find as much gold as you can and avoid any possibility of being eaten by a tiger, which door(s), if any, should you open?

Door 1 If a tiger is behind door 4, then it is the only tiger. |
Door 2 If there is only one tiger, then it is behind door 3. |
Door 3 If gold is behind door 1, then more than one door leads to gold. |
Door 4 If more than one door leads to gold, then door 2 leads to a tiger. |

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Answer:

Suppose there is a tiger behind door 3. Then its statement is false; it can only be false if gold is behind door 1 and no more than one door leads to gold – in other words, gold is behind door 1 and tigers are behind the other three. Specifically, there is a tiger behind door 4, but the statement on door 1 says that if a tiger is behind door 4, then it is the only tiger. This is false, but a door leading to gold should have a true statement. This is a contradiction, so there must be gold behind door 3.

Suppose there is a tiger behind door 4. Then its statement is false; it can only be false if more than one door leads to gold and door 2 does not lead to a tiger. In other words, door 2 must lead to gold. The statement on door 2 must be true, so if there is only one tiger it is behind door 3. We know that there is gold behind door 3, so there must be more than one tiger, so another tiger must be behind door 1. So if there is a tiger behind door 4, then the order of the doors is tiger, gold, gold, tiger.

Suppose instead that there is gold behind door 4. Then its statement is true, and since more than one door leads to gold, door 2 must lead to a tiger. Since there is no tiger behind door 4, the statement on door 1 is vacuously true and must lead to gold. So if there is gold behind door 4, then the order of the doors is gold, tiger, gold, gold.

We do not know which of the two situations is correct. Every door could lead to gold or a tiger except for door 3, which must lead to gold, so that is the only door you should open.