New logic puzzle posted! Tiger Bait 8

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Tiger Bait 8

 

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.

Door 1. An orc is behind one of these doors.

Door 2. A dragon is behind one of these doors.

Door 3. If a tiger is behind door 1, then a tiger is behind door 2.

Door 4. A tiger is behind door 2.

Which door leads to the gold?

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

 

 

 

 

 

 

 

 

 

 

 

 

 

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Answer:

Suppose the gold is behind door 1. Then the statement is true, and an orc is behind one of the remaining doors and tigers are behind the other two. Consider the statement on door 3: it can only be false if both a tiger is behind door 1 and a tiger is not behind door 2. Since a tiger is not behind door 1, the statement is vacuously true, so the orc must be behind door 3 and tigers are behind doors 2 and 4. But then the statement on door 4 is true, which is impossible if a tiger is behind it. Therefore, the gold is not behind door 1.

Suppose the gold is behind door 3. If either a dragon or an orc is behind door 2, then a tiger would have to be behind door 1, making the statement on door 3 false, so a tiger must be behind door 2. So the statement on door 2 is false, and the remaining doors lead to two tigers or an orc and a tiger. But then the statement on door 4 is true, which is not possible for either an even-numbered door leading to an orc or a door leading to a tiger. Therefore, the gold is not behind door 3.

Suppose the gold is behind door 4. Then its statement is true and there is a tiger behind door 2, and since the statement on door 2 must be false, no door leads to a dragon. Since there is a tiger behind door 2, the statement on door 3 is necessarily true regardless of what is behind door 1, so door 3 can’t lead to a tiger; it must lead to an orc. But then the remaining tiger is behind door 1 and the statement on door 1 is true, which is impossible. Therefore, the gold is not behind door 4.

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Having eliminated all of the other doors, the gold must be behind door 2. Therefore, a dragon and two tigers are behind the remaining doors. The dragon cannot be behind door 1 because then door 3 would lead to a tiger and the statement on door 3 would be vacuously true, but we have no way of knowing whether the dragon is behind door 3 or door 4.

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