>I already told and everyone already guessed, that 99 have 100% to survive and the last one has 50% probability.

I *THINK* I have it. You have no idea how many different groups of binary numbers I put together trying to see a pattern that can be discernible by a single bit answer.

The last sage says White if there is an even number of white hats ahead of him or black if there is an even number of black hats.

Sage 99 counts the number of black or white hats ahead of him and he can tell immediately if he's black or white.

The rest keep track of the previous answers and so on.

This better be it!

alex