The Tunnel

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Malenkov knew he was smudged only because the other two did not claim the same!

explanation : if Malenkov is not smudged, then Molotov can see so, and yet he finds Vishinsky with his hand raised. Which tells him (Molotov) that Vishinsky has raised his hand on seeing Molotov's smudged face, so Molotov should have claimed that he himself was smudged. The fact that he did not so claim, shows that he was confused whose smudged-face was prompting Vishinsky's raised hand. Hence Malenkov is convinced about his own smudge.

Thanks,
R.N.Radhakrishnan
Hyderabad, India.

This is correct. At first, the puzzle apears insoluble since the situation is perfectly symmetric, and nobody has access to any information not held by the others. Solving it requires "stepping back" and thinking about what the other Russians could be thinking... In case the answer above isn't immediately clear, try considering the 2 possibilities where all three have raised their hands:

1. Only two people were smudged. Those two would have seen that one person was not smudged, and would have deduced that they themselves must be smudged because the person they see as smudged has their hand up. They would then have lowered their hands.
2. All three were smudged. All three could have realised that this was the case, and lowered their hands.

It seems to me that this puzzle hinges on the assumption that these are three intelligent people; case #1 would have been immediately clear to them. The fact that the others didn't immediately put down their hands was the clue that the situation was perfectly symmetric...

Dissenting View

With reference to your Russian tunnel problem I slightly disagree with your answer basically due to the wording of the question. The only way that Malenkov could have known if he was smudged was if one of the other 2 wasn't smudged. The other smudged face could obviously have also realised this but there is no indication that they would continue to drop their hands once they had realised as Stalin had only asked for someone to drop their hand once they were certain on whether they were smudged or not. This is essentially the same as the original response.

Scenario 2 however, with all 3 smudged, is incorrect as none of them can know for certain whether he is smudged or not. To be absolutely certain would require relying on the intelligence and lateral thinking of the others to make the claim before Malenkov. Otherwise if Vishinsky or Molotov for example weren't smart enough to claim that they knew they were smudged because Malenkov wasn't then Malenkov would have to rely on the fact that they were smart enough to work it out. I'm basing this argument on the fact that VIP means Very Important Person which we all know doesn't equate to Very Intelligent person.

John McCall
North Sea
Scotland

And here's another twist, from M. Lyons:

I have another solution. It requires deductive thinking on the part of the russian who raised his hand.

He can see both of the other men's faces, and sees that they are smudged. He can also see their hands, and can see that both other men's hands are sooty also. He CAN see his own hand, which is sooty. He can therefor conclude, logically that A) We were all in the same car, on the same train, at the same time, going through the same tunnel. Both of the others got soot all over their bodies, including head and hands. B)I did nothing to prevent myself from getttin soot on my face, and C) I can see that my hand is sooty. Therefore, it is logical that I also have soot on my face.

The fact that he is the first one to lower his hand is a testament to his own quick thinking.

Stalin then promoted him to some important position, and he was later executed. The other two men lived long lives of obscurity as factory workers.