>>If you heard these puzzles before or it's too simple for you, please, don't answer, and let the others solve them
>>
>>I translated these puzzles from Russian (though the second one
>>originated from English book), so, please, if you see problems in my English, correct them right away.
>>
>>Puzzle 1:
>>
>>100 sages stay in a row. Each sage wears a hat, which might be either white or black. Each sage can see everyone, who stays before him, e.g. the last one sees 99 sages, 99th sees 98 and so on...
>>
>>They have been told, that each sage, who identifies his hat's color incorrectly, would be killed. They have a minute to find a best strategy (discuss this situation among them). They should pronounce loudly the color of his hat starting from the last one to the first one (each one hears, what the other say). Now the question: How many sages can survive and what would be their strategy?
>>
>>
>>Puzzle 2.
>>
>>One person was lost in a forest. He knew, that there are two villages near the place, he was lost. In one honest people live, who always tell the truth. In the other, in opposite, knaves live, who always answer false. He met a person on the crossroad and asked him just one question, which helped him identify the correct road. What was the question, he asked?
>
>Puzzle 2 is not clear. Is the lost person trying to find his way to one of the villages? Or a third village?
>
>Update: I suppose if he can get to the 'honest' village they will help him get home...
>
>So you ask "Do you live down this road." If he says Yes, you take that route. If he says NO, you take the opposite route.

Yes, this is a correct solution. I solved it a little bit differently and more complicated, but my colleague solved it exactly the same way and I like this solution better, than mine.