Posted by T.Gracken on August 13, 2001 at 22:19:49:
In Reply to: ??? are you sure posted by brent on August 13, 2001 at 20:25:43:
: Just a sec - let's label the men 3-2-1 from back to the front - 3's response can only be dunno - the only impossible combo in front of him is two white hats - otherwise he answers black.
: But to say:
: "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)"
: is making an assumption - there is a possibility that 2 has on EITHER black or white, his answer is correct as dunno - but - 3's answer leaves two possibilities. There are three black hats and one white hat or two of each as possiblilities for 2 to see, reguardles of what he is wearing, and reguardless of 3's answer (unless 3 had answered black). I believe your logic is flawed in assuming 2 saw a black hat on 1. In other words - 2 could not draw a conclusion from what he saw or heard unless 3 had answered black. How can 1 draw any conclusions when he has no elimination of possibilities as visible evidence and 3 and 2's answers still leave him the same possibilities that 2 faced with the advantage of the elimination of one hat?
: But past that - I have no better answer - lol. What does the poster of the riddle have to say reguarding a solution?
: Or am I missing something?
you're missing something.
Since 3's answer was don't know; as stated by Mr. Khan, 1 and 2 CAN'T BOTH be wearing white. (otherwise he'd know he was wearing black...)
so that leaves either
1 is wearing white and 2 is wearing black,or
1 is wearing black and 2 is wearing white, or
1 and 2 are both wearing black.
If 1 is wearing white then 2 knows that he (that is 2) is wearing black.
...better?