>>Puzzle 1:
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>>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?
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>All can survive if they form a circle.
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I like this one :) Though I'm not sure, it was permitted. Let's assume, that they can not change the figure and must stay in a row.

>>Puzzle 2.
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>>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?
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>Which villiage to you live in?

How this question would help him? Though you're close.