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#919
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Maybe I'll wait a bit longer before providing the voiceover and just say that the closest correct answer is what Uranium235 wrote.
Uranium235
I have a feeling that the answer is that 99 people can be saved, but only one has a chance to be saved.
This is based on my memory of the problem; I don't remember the solution.

Yes. 99 people are guaranteed to be saved, and one has only a chance!
Uranium235
The first person to answer knows the number of hats of each color for 99 people.
The second person to answer knows the number of hats of each color for 98 people, plus the first person's answer, and whether or not the first person was executed.
I'll figure out how to put this into a formula, or maybe I won't.

This contains everything that's needed and even some extra information. Maybe you can try to figure out how each person can determine the color of their hat based on what the wise men said before them and the colors of the hats of those standing behind them?
Всё не так плохо как Вы думаете. Всё намного хуже!