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A computer game involves a knight on a quest for treasure. At the end of the journey, the knight approaches two doors.

The left door has a sign saying "One of these doors leads to a ferocious dragon!" and the right door has a sign saying "Behind this door is treasure, and behind the other door is a ferocious dragon!"

A Servant informs the knight that one of the doors is true, and the other is false. Use Indirect Reasoning to determine which door the knight should choose. Explain your reasoning.

Where do I start? I'm confused on where to begin and the steps to figuring out the right door...

Frank
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    Assume the dragon is behind the left door and try to think about the implications of this assumption regarding the truth. – Dark Jun 01 '16 at 17:27
  • Well if the first door is false then the second door is also false... – Ali Caglayan Jun 01 '16 at 17:27
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    An interesting thing to think about: Does "one" imply "only one?" Can there only be one object behind each door? – Hrhm Jun 01 '16 at 18:58

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Suppose the second door is being truthful. Then the first door has a dragon behind it. So, there is a door with a dragon. So the first door is being truthful too. This contradicts the servant.

Hence the second door is lying, but the first door is telling the truth. Unfortunately, as the questions is set up, this means the statement "door 2 has treasure and door 1 has a dragon" is false. This could, however, be false if door 2 was safe, but there was no treasure. So it seems to me like there still could be a dragon behind door 1, provided there is no treasure behind door 2. Or it can be because there is a dragon behind door 2.

James
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Another solution would be for both doors to lead to a dragon, which would make the left door true and the right door false.

Stella Biderman
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    Tricky. But I'd argue "One of these doors has a dragon" to mean exactly one and not "at least one". But it is debatable. – fleablood Jun 01 '16 at 17:50
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1) how do we know the servant is telling the truth and/or is correct. 2) "at the end of the journey" ... does that mean as we haven't found the treasure yet that the treasure must be behind one of the doors because the treasure must be in the game somewhere?

I'm going to assume the servant has to be telling the truth and that the treasure must be behind one of the doors because .... well, puzzle ...

As the circumstance of Door 2 (Door 1 has a dragon and treasure behind 2) is a subset of circumstance of Door 1 (one door has a dragon). Door 2 is true only if Door 1 is. As only one is true Door 2 can't be true. So Door 1 is a lie.

So one door has a dragon and it's not the case that Door 2 has the treasure while Door 1 has the dragon.

That leaves 3 possiblities.

A) Door 1 has the dragon and treasure and door 2 is empty of anything pertinent.

B) Door 1 has the treasure and door 2 has the dragon.

C) Door 2 has the dragon and the treasure and door 1 is empty of anything pertinent.

(D) Door 2 has treasure and Door 1 dragon is impossible)

So open Door 1. It might have the treasure without a dragon, and if it does have a dragon it will have the treasure. If it's empty... well, no loss. You might get the treasure without a fight and if you do face a dragon it will have the treasure.

If you open door 2 you might have to fight a dragon unnecessarily when you cou'd have had the treasure no problem. You will not get the treasure without having to fight a dragon.

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If there's a possibility there is not treasure. Well, You have to decide if it's worth risking a dragon for a potential treasure. If it is pick door 1. If there is not treasure you're going to try both doors and fight the dragon anyway. If there is a treasure Door 1 has the only possibility of not needing to fight the dragon and door 2 has the only possibility of fighting a dragon without the treasure.

If it's not worth risking a dragon. Well, Door 1 is the least risky but picking neither is less risky than that. There is definately a dragon behind a door but not nesc. a treasure.

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So what if servant is lying or wrong. Well, then you have to figure out the trustworthyness of doors and servants. It'd be interesting, albeit it far fetched if servants and doors are equally likely to tell truth or to lie and that doors are equally likely have treasures and/or dragons as not.

Not the puzzle asked but could be fun.

fleablood
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