100 Hats

doctorj said:

Actually... if the guy in middle realises that the guy at the back hasn't said anything, it must be BW or WB. If he sees the hat in front is B, he would know his must be W, but because he didn't call out, it leaves two possibilities - WW or WB. Which tells the guy in front his must be white.

How can the poor guy in the middle guess correctly?

Click to expand...

You are right, but left some possibilities out.

If the guy at the back didn't answer, then the two in front can be WB, BW or WW. It's agreed that BB is not possible because being a wise man he should have immediately known that his hat must be white and would have answered within a short time.

Because there was no answer after a short time, the two in front deduced that only the above 3 outcomes were possible.

After another short period had elapsed, the guy in the middle should have then deduced that his hat must be white if the guy in front had a black hat. But as he didn't answer either, the guy in front was able to deduce that the only possibility was his hat must be white.

Key to the problem is that they are WISE men.