>>Yours or Mark's solution could not be accepted, because the observer can easily understand this trick and as I said, the cheating is not allowed.
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>Nadya,
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>I really was only kidding, but since you pressed it...
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>I think that the 99 sages all taking the time to count after each one determines their hat color might just alert the observer, as the 2nd sage would need to spend a much longer time than the 2nd to last sage (counting 98 hats vs counting 1 hat). I think the observer might have a clue that something was going on. Like cheating? Of course, I guess they all could have tried to wait the exact same amount of time as the 2nd sage so it woudn't be obvious, but then the first sage would have to take a guess as to how long it would take the 2nd sage to count and make sure their pause was at least that long or longer. :)
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>Again, you were looking for one, mathematical/programmatic answer, but if you look deep enough, and from different perspectives, it has flaws also. Remember, I already conceded that your answer was correct because you knew what you were looking for and were also the final judge in the matter. It was fun trying to figure out the right answer though - thanks!
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>Renoir

Renoir,

The last person (the person at the back of the line) has to count everyone in front of him before he starts. Everyone else would count the ones in front of them at the same moment...that information does not change as the sequence progresses.

So there would be no need for delays once the first sage says 'Black' or 'White'. A delay at the beginning would be understandable...the first sage is making a life or death guess *grin*. So this strategy is not observable...

However, I agree with you. If they are given a minute to devise a strategy, why would it be *cheating* if it was observable? (As in the voice inflection method). They would have to be told in advance (before devising strategy) that they are not allowed to make any additional noises, or to use voice inflection.

Still, an interesting problem. Thanks again, Nadya.