I hate this!!!! ;-)

OK, here's a programmatic solution that will give 50% chance to 1/3 of the sages and 100% to the other 2/3.

It's loosely based on the delta-sigma algorightm, which is used for doing Analog to Digital conversions.

The first sage of every group of 3 states whether the next two hats are the same or different.

The second sage, by looking at the third guy's hat and knowing the answer of the previous sage he can tell whether his hat is different or the same.


Another possibility is that the first 6 sages volunteer to state colors to indicate in binary code how many black hats are from the 7th to the 100th sage.

Let's say there are 43 black hats. 43 = 101011 so they say BWBWBB.

Now all the others have to do is count how many black hats are ahead of each, keep track of how many have said black before them and get over with it and I can go to have lunch and back to work!!!!! ARRRGGHHH!!!!

Alex