Tiger Bait Logic Puzzle #13 – Hard Logic Puzzles

Looking for hard logic puzzles? This may be the most difficult printable logic puzzle we’ve shared!

You are standing before four doors in a row. Gold is behind one door, a dragon is behind another, and tigers are behind the other two. A statement on a door leading to gold is true; a statement on a door leading to a tiger is false. You do not know anything about doors leading to dragons.

Door 1Door 2Door 3Door 4
A dragon is behind this door.

 

Unfortunately, someone has torn the signs from three of the doors, leaving them scattered on the ground. You have no way to tell where the signs originally belonged.

First sign: The gold and the dragon are behind adjacent doors.

Second sign: If a tiger is behind the door immediately to the left of this one, then gold is behind this door.

Third sign: A dragon is not behind the door immediately to the right of this door.

 

Luckily, an old knight is standing nearby. You recognize him as someone who always tells the truth and you ask him on which doors the signs are supposed to go. He says, “I remember that the third sign wasn’t on the fourth door. That wouldn’t have made any sense if it were because there’s no door to the right of it. I don’t remember where any of the signs actually were, but I do remember that when I knew where they were supposed to be, I was able to figure out where the gold was. The gold is still there, by the way.”

Which door leads to the gold? (Aren’t hard logic puzzles fun?)

Scroll down for the answer!

 

 

 

 

 

 

 

 

 

 

 

 

 

 


The answer to this printable logic puzzle:

Since the third sign can’t go on door 4, there are four possible permutations:

  • First, third, second
  • Second, third, first
  • Third, first, second
  • Third, second, first

Let’s go through them and answer this logic puzzle!

First, third, second

Gold can’t be behind door 1, because then it would have a false statement. If it’s behind door 2, then it must have a dragon adjacent. If the dragon is behind door 1, then doors 3 and 4 must lead to a tiger – but then door 3 has a true statement, which is impossible. If the dragon is behind door 3, then door 4 must lead to a tiger, but then the statement on door 4 is vacuously true, which is impossible. So, the gold is not behind door 2. (Hard logic puzzles like this one may seem impossible…keep reading!)

If the gold is behind door 3, then the statement on door 4 is again vacuously true, so it must lead to a dragon. But then door 2 must lead to a tiger, and the statement on door 2 is true, which is impossible. So, the gold must be behind door 4. The statement on door 3 is then true, so it must lead to a dragon. But then door 2 must once again lead to a tiger and once again have a true statement. Therefore, gold can’t be behind any of the doors and ABC is not a possible permutation of the signs.

Second, third, first

Under this permutation, gold could be behind door 2 (and a dragon behind 4) or it could be behind door 4 (and a dragon behind door 3). The proof is left to the reader. But this means we can’t tell which door leads to the gold, so this is not a possible permutation.

Third, first, second

Under this permutation, gold could be behind door 2 (and a dragon behind door 4) or it could be behind door 4 (and a dragon behind door 2 or door 3). Once again, the proof is left to the reader, and once again, since we can’t tell which door leads to gold, this is not a possible permutation. (Hard logic puzzles are fun, yea?)

Third, second, first

As before, gold can’t be behind door 1. If it’s behind door 2, then it must have a false statement and there is not a dragon behind door 3, so that door must lead to a tiger. But then the statement on door 3 is vacuously true which is impossible.

Suppose the gold is behind door 3. Then the statement on door 2 is true, so it must lead to a dragon, and tigers are behind doors 1 and 4. But that makes the statement on door 4 true, which is impossible.

Therefore, door 4 must lead to gold. Its sign is true, so the dragon must be behind door 3. Tigers are behind doors 1 and 2 and their statements are false, so it all checks out.

So: third sign, second sign, first sign is the only permutation that gives us a clear answer as to which door leads to gold, so according to the knight it must be the correct permutation. The complete solution is:

Door 1: A dragon is behind this door. TIGER

Door 2: A dragon is not behind the door immediately to the right of this door. TIGER

Door 3: If a tiger is immediately left of this door, then gold is behind this door. DRAGON

Door 4: The gold and the dragon are behind adjacent doors. GOLD

Check with us daily for hard logic puzzles like this one! Remember, you can print this daily puzzle too! And don’t forget to check out our logic puzzles for Android app!

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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