Puzzle 40 Solution

The last person will make a count of the total number of black and white hats. If there is an even number of black hats, he will say "black". If there is an odd number of black hats, he will say "white". Thus, the next person in line will work out the number of black hats in front of him and determine whether his hat is black or white. Similarly, everyone else in line can work out whether his hat is black or white based on the previous answers.

Here is an example. Lets say the last person counts 80 black hats and 19 white hats. He says "black" which means there are an even number of hats. The next person in row will count the number of black hats.

Let's say he has a black hat. Then he will count 79 black hats before him. But the number of black hats (including his own) is supposed to be even, so he deduces he has a black hat.

If he has a white hat, he will count 8o black hats before him. Thus, he must not have a black hat or else the last person would have counted an odd number of black hats. He deduces he has a white hat.

Hence, all the remaining 99 wise men can work out their hat colour in this fashion.

Answer: 99