>>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?
>
>If there are 50 black and 50 white, and they know this, then they all survive. Can the 100th sage shout out how many of each color he sees before guessing his own color? If so, then the 100th sage has a 50/50 chance of survival, while all the others can survive.
>

Incorrect. First, there could be any number of black abd white hats (e.g. they all could be in white - the hats color are random). Secondly, he should say only color Black or White (he is not allowed to say something else). However, "Black" or "White" could be a code for other. You correctly guessed, that 99 will survive and the last one has 50% probability of survival. Now you should find out the 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?
>
>Do you live down this road? If he answers No, then proceeds to follow it, take the other road [he answered falsely]. If he answers Yes, then follows it, follow him [he answered truthfully].

I don't follow your logic, but I doubt, you're correct. He doesn't need to follow him to find out, if it was true or false...

Think again.