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GentlePurpleRain
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The last question to the guards

"What will happen next?" asked the old man. His voice was friendly, his eyes bright, as always. His hair and beard seemed to be even whiter than ever before.

"The standard procedure is as follows: New arrivals are subject of a test after they are guided to the big hall with two doors and two guards. One door leads to heaven, the other to hell. One guard always tells the truth, the other is lying all the time. They are simple guys, and can only answer with yes or no. The test subject has to ask a single question that makes him able to identify the door to heaven."

"Oh, I've heard about that."

"Sure you have. We know you are familiar with this kind of situation. But let me clarify: The guards cannot answer hypothetical questions about their own answers. Those just break their mind. They are simple guys, as I mentioned. They can answer hypothetical questions about each other's answers though, as those do not need that much abstraction. They both know if the other one is a truth-teller or a liar, so have all the information that allows them to answer these kind of questions."

"That shouldn't be a problem."

"Sure. We know your skills in the subject. That's why we made it a little bit different for you. It should be a serious test, shouldn't it? There is a third guard in the hall this time. He is either a truth-teller or a liar, but I won't tell you which. However, the other guys know his type, and he is aware of theirs. He will be dressed like the other two guards, so they are all indistinguishable. You are allowed to ask two questions, but they cannot be addressed to the same guy. All you have to do is to identify the door to heaven. Shall we start?"

"I'm looking forward to it."

There they were. The famous hall. The old man and the guide were facing the guards. They both enjoyed the moment - it was something special for both of them after all.
The old man finally went up to one of the guards and asked something. The guard answered. The old man turned to his guide.

"I think it's all just the standard procedure from now, once we send out that guy," he said, pointing to one of the guards.

"Sure, Raymond. You have passed the test," answered the guide, and opened the door to heaven.

What was the question the old man asked the guard, and what conclusion did he reach from the answer?


Raymond Smullyan, the brilliant mathematician, who was well known for his 'Knights and Knaves' extensions of the classic puzzle, passed away at the age of 97 on 6th February 2017.
This simple puzzle is my modest personal tribute.

elias
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