yamits

Since everyone sees every other person's colour on the way to the King, they should each tally up the amount of black-coloured doors and white-coloured doors and tell the King the colour that are on MOST doors. E.g. If a prisoner sees 52 black doors then he should answer 'black'. Using this method, the majority of prisoners will get their colour right.

This method will absolutely work for all situations except for one. The exception is when there are 51 whites and 50 blacks (or vice versa). In this case, all prisoners with black doors would be wrong and and some of the prisoners with white doors (facing a 50-50 proposition) will also be wrong -> Majority will be wrong.

However the chances of painting 51 whites and 50 blacks (or vice versa) is extremely small:

Probability = (101 C 50) / 2^101 = slightly less than 8%

Thus this is likely the optimum strategy. (RIght? LOL)

Could Mr Poster plz reply to see if this analysis is right?