New logic puzzle posted! Tiger Bait 9

Tiger Bait 9

 

You are faced with 4 doors. One of them leads to gold. Two of them lead to tigers. The remaining door leads to a tiger, an orc or a dragon.

The statement on the door leading to gold is true. The statement on any door leading to a tiger is false. The statement on any odd-numbered door leading to an orc is true. The statement on any even-numbered door leading to an orc is false. Nothing is known about doors leading to dragons.

Which door leads to gold?

Door 1. If gold is behind door 3, then no door leads to a dragon.

Door 2. If gold is behind door 4, then no door leads to an orc.

Door 3. No door leads to an orc or a dragon.

Door 4. A tiger is behind door 3.

Check out the discussion on Reddit or scroll down for the answer.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

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Answer:

Suppose the statement on door 3 is true. Then, since no door leads to an orc or a dragon, door 3 must lead to gold and all other doors lead to tigers. But this makes the statement on door 4 true, which is impossible if it leads to a tiger. Therefore, the statement on door 3 is false (and does not lead to gold) and one door leads to an orc or a dragon.

Door 3, with its false statement, can’t lead to an orc. Suppose it leads to a dragon. Then the statement on door 4 is false and does not lead to gold, it must lead to a tiger. But then the statements on doors 1 and 2 are both vacuously true, even though one of them must lead to a tiger. This is impossible; therefore, door 3 must lead to a tiger.

This makes the statement on door 4 true, and it must lead to gold or a dragon. Suppose it leads to a dragon; then the statements on doors 1 and 2 are once again vacuously true, which is once again impossible since one of them leads to a tiger. Therefore, door 4 leads to gold.

Door 1, incidentally, leads to an orc. The proof is left to the reader. 🙂

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The puzzlemonster. Lifelong puzzle maker, animal lover, total nerd. Husband to Android developer.

About Eric

The puzzlemonster. Lifelong puzzle maker, animal lover, total nerd. Husband to Android developer.

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