Can you solve this puzzle ?

[ilyacine]

that dos not matter

If Prisoner B said in open (in present of A & C),that his assumption/answer is Black hat,that does not give any extra hints for Prisoner A & C,cause they already can see : B wared White Hat

Same thing applied for Prisoner C to.

Even if no one revealed his thought, the other 2 still could have an idea of what he thinks his color is because he didn't won (no clue is a clue) .

[sohom]

friend where r u?
give the proper answer

[superstar]

i think the answer is black hat as both gave the answer wrong because they saw 1 black and 1white for them chances were 50/50 but he saw two whites

[ilyacine]

I'm going to add some hints right now, solution after 24 hours

---------- Post added at 10:07 PM ---------- Previous post was at 09:16 PM ----------

EDIT: extra hints:

In order to solve the puzzle you need to pay close attention to every single word.
1 - Saying that the winner figured the solution out after "quite long time" is actually a factor key, it means that the two others are unable to solve it no matter how many time we give theme (extremely important hint)
2 - The best & less complicated way to solve this puzzle is assuming that you are the winner and think how can you actually know for sure your color, this is done by trying to find out why the 2 other prisoners couldn't get the answer, the best way to do that is to think as the winner will, ie trying to think what the 2 others are thinking, and you already now that they are incapable of finding out their own colors.
3 - It's very important to know that if the winner is seeing other than 2 whites, he will never be able to win (except if he sees 2 blacks which is not a puzzle).
4 - Again it's not a probability puzzle, you can assume what ever you want, but don't start with probability of 1/3 or 1/2 ...etc, it will never work.
5- If you're enable to find the solution you could assume a wrong solution, if you can prove it to be wrong then the opposite is the right solution i.e : the winner could only have a white or a black hat, if you can prove he's not wearing a black one, than a sure thing is he's wearing a white one ! and vis versa.

Good Luck !

[cotufa-ssdd]

So, the first man didnt know what hat color he had on, which means he did not see 2 black hats otherwise he would have a white for sure.

The second man knew that the first man did not see 2 black hats in front of him, so he knew that the first man must have seen either 2 white hats or a white and a black hat, the man in the middle knew that if he see a black hat in front of him he than he MUST have a white hat on, but since he didnt know what hat he had on, it means he did not see a black hat in front of him, analyzing this, the last man knew he had a white hat on.

[wtg]

Wow, these hat puzzles were from the 1960's
we were taught how to solve these induction puzzles using Hamming Codes as part of a course including lost data bits in transmission years ago (seem to recall a 10 "hat" variation being in an exam paper).....

Think wide guys - It's easier than you think

[ilyacine]

The second man knew that the first man did not see 2 black hats in front of him, so he knew that the first man must have seen either 2 white hats or a white and a black hat, the man in the middle knew that if he see a black hat in front of him he than he MUST have a white hat on, but since he didnt know what hat he had on, it means he did not see a black hat in front of him, analyzing this, the last man knew he had a white hat on.

Sounds like summarized solution
Although you had almost everything right, you didn't explain why "the man in the middle knew that if he see a black hat in front of him he than he MUST have a white hat on"

[kaizer01]

@ilyacine
give the answer now

[IntelliTool]

We have three guys, me, john and jack.
I know, John and jack are wearing white hats.
So, i have either a black or a white hat.
Same goes for jack and john, they both see only 2 guys with white hats.
If i'd see 2 black hats, i'd knew that i have a white one.
in all other cases, it is unclear if i have a white or a black one.

Jack looks at the hats. He doesn't see 2 black hats, so he has no solution.
John looks at the hats, he knows, he'd either see 2 white or 1 black and 1 white hat. (The "no-solution" cases, since jack didn't have a solution)
If he'd see a black hat on me, john would know that he has a white hat on (cus if i had a black hat on me, and john too, jack would have known that he cannot have a black hat)
Since he's looking at 2 white hats, he also has no solution.
So i know, i don't have a black hat on, since a black hat on me, would have meant, that john would have a solution.

So, after a time I'm sure that Jack and John aren't able to figure out what kind of hat they have, that means for me, i have a white hat on.
i take my educated guess and get free.

[cotufa-ssdd]

Sounds like summarized solution
Although you had almost everything right, you didn't explain why "the man in the middle knew that if he see a black hat in front of him he than he MUST have a white hat on"

ofcourse i did:

since the first man didnt know what color hat he had on, the man in the middle knew that he didnt see 2 black hats (since there are only 2 black hats, if the first man saw 2 black hat then he would have known he had a white hat) so the the man in the middle knew the first man saw either 2 white hats, or 1 black and 1 white hat. With this the man in the middle knew that there could ONLY be ONE black hat or 2 white hats. So if the man in the middle saw a black hat in front of him then he would have to have a white hat! but since he didnt know what hat color hat he had on, it means he did NOT see a black hat in front of him, he must have seen a WHITE HAT.


i cant explain it more then that!