Posted by Subhotosh Khan on August 08, 2001 at 14:55:04:
In Reply to: Re: logic, intuition, and serendipity posted by T.Gracken on August 08, 2001 at 07:18:10:
: : a box contains three black and two white hats. three men standing in a line are facing forward and can see only the person or persons in front of them. each of the three men has one of the hats placed on their head but does not see which color. each man can, however, see any hats in front of him on another man, and each knows what was in the box. when the man in the rear is asked what color his hat is, he replies, "i don't know". when the man in the middle is asked he answers "i don't know". when the man in front is asked, he replies, "mine is black and that is no guess". he is correct. how did he know???????
: perhaps he is standing in front of a mirror...
: Of course, my question about your question is: what do you mean by "facing forward?" Is there such a thing as "facing backward?"; or sidways...
Leaving aside TG's suggestions (mirror or facing siseways)and assuming all these people are intelligent and truthful:
The third person saw either saw two black hats or one white and one black on (1)and (2).
The (2) did not see a white hat on (1) - otherwise he would have known that he was wearing a black hat (from 3 s response)
- So -
A black hat is on (1)