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Solutionless Riddle in the Cloudpeaks?

Contains spoilers!
[spoiler]So, I was travelling to the Cloudpeaks and reached a cave. Two men were imprisoned in trapped cages.
If opened one of the doors free them both, the other kills them both. Now, they know which one is right but will only answer one question for me to find out. And one of them will be lying.
Basically, I need to ask a question whose answer will both determine whether the answerer is lying (#1) and his opinion about the right door (#2).
But, I only get to choose questions where one or the other point is answered:
- Is your cage the one that's trapped? #2
- Is the other cage the one that's trapped? #2
- Which cage will the other tell me is safe to open? #2
- If I ask the other prisoner, will he tell me the truth? #1
- Which of these cages is not trapped? #2
- Are you lying to me? #1
What kind of fool does this game take me for? These suggested questions are all the same![/spoiler]

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