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Can you solve this puzzle ?

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ilyacine

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Can you solve this puzzle ? (Solution revealed)

Good evening, ladies and gentlemen. We are tonight's entertainment, i only have one question: "how did he solve the puzzle ??"

First the rules:
No google, no youtube, bing :P or what soever.
This puzzle doesn't need any sort of knowledge about probabilities or mathematics, it is only about LOGIC, and that's why i love it so much, just think logically and be patient, the answer is quite tricky.

The puzzle:
We have 3 prisoners, and there is a decision about letting one of them go free, since it's not fair to leave it to chance, we've come out with an idea: We show the 3 prisoners 5 hats, 3 of them are white, and the other 2 are black.
we put a hat on each one's head, the prisoners now can see each other's hat but they can't see their own hat.
we give them one chance to guess their own hat's color, the first one to guess his color right will be freed, but he has to explain how he got it, if he just got it by chance or if he was wrong the prisoner will get 3 more years of prison.
After quite long time, one of them got an idea and he guessed his own color right !
His only clue was that he could see 2 whites on the 2 other prisoners, yet he could never see his own color.
So how did he do it ?

Remember :
- No googling, just try to solve it by yourself.
- This is NOT a problem of probabilities, it's just about LOGIC.
- Kindly if you already know this puzzle leave the chance to the others, this is a modified version of the 3 prisoners puzzle, the original one is just mathematics, this one it just a matter of logic.

Good luck ;)

*====================================*

If you couldn't solve it, here's some clues to guide you:
here

If even with the hints you couln't solve it, here's the complete solution, hope you enjoyed the game.
here
 
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44 comments
Reserved post. Started solving.

Edit. aah wait. I remember this problem. This is just a variant of the earlier one.
 
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good 1 @op

that freed prisoner can ask others prisoner about whether their hats color matching or not?
 
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Nitish said:
Edit. aah wait. I remember this problem. This is just a variant of the earlier one.
Click to expand...

So, do you still remember the solution ?

---------- Post added at 09:29 PM ---------- Previous post was at 09:26 PM ----------
sohom said:
good 1 @op

that freed prisoner can ask others prisoner about whether their hats color matching or not?
Click to expand...

No one will answer no one, they're all trying to get out, so any further information they give increases the chance of the asker solving the problem.
 
How did he do it
cuz there were 5 hats 3 white and 2 black according to the puzzle. The two black hats wernt used so the prisoner just made a lucky guess.that maybe his hat was also white as there were 3 white hats
 
^^Nice try but nope :P
if he just got it by chance or if he was wrong the prisoner will get 3 more years of prison.
Click to expand...

He had to explain how he got it, otherwise he'll spent 3 more years in prison.
 
Well, either story isn't told correctly, or there is no chance to say the solution, without including the highest probablility factor.

If none of them tried to guess loud, or he couldn't see remaining hats, there is no LOGICAL solution, except probability, where there's a chance of 2:1 that he's wearing black hat.
 
Lol, certainly not.
Actually the key is in this sentence:
After quite long time, one of them got an idea and he guessed his own color right !
Click to expand...


---------- Post added at 10:35 PM ---------- Previous post was at 10:28 PM ----------
cvrle77 said:
Well, either story isn't told correctly, or there is no chance to say the solution, without including the highest probablility factor.

If none of them tried to guess loud, or he couldn't see remaining hats, there is no LOGICAL solution, except probability, where there's a chance of 2:1 that he's wearing black hat.
Click to expand...

Yes, there is a logical solution, actually even if they didn't guess out loud he could know what they're thinking/guessing, and here i revealed 50% of the solution >_<
 
Prisoner A sees 2 white hats
Prisoner B sees 1 white 1 black
Prisoner C sees 1 white 1 black

or

Prisoner A sees 2 white hats
Prisoner B sees 2 white hats
Prisoner C sees 2 white hats

3 white hats, 2 black
2 white hats on head / leaves 1 white and 2 black in the game
(trying to solve)

In case where someone sees black/white hats on opposite sides (B and C see black white), they're not able to solve the answer, because there could be any color on their head. Also, 2 persons could guess. This option is self excluding for persons B and C
In case where someone sees white/white combination, there's still one white left and 2 black, as possibility. Therefore, also unable to solve it. 3 persons have equal chance in solving it, since they all see the same, and can think the same.
Since solution MUST have an answer, the only way is that persons B and C see white/black combination, where A person is the person with black hat.
 
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After going to wikipedia a crucial thing got left out of this.

edit: nvm. If they can all see each other it can be guessed correctly indeed.
edit²: still not sure tho.

@OP: what in this situation:
A: white
B: black
C: white
 
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spent last 15 minutes on this, and still no clue.

Alternative answer- since the prisoners can see each others hat, they are sitting in a circle, And one prisoner was able to see the reflection of his hat in the eye of other. (but i guess they are too far apart to do this :P ).


White hat , black hat , Is This SEO related question <!-- too tired to think -->
 
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Now we're talking !
cvrle77 said:
In case where someone sees black/white hats on opposite sides (B and C see black white), they're not able to solve the answer, because there could be any color on their head. Also, 2 persons could guess. This option is self excluding for persons B and C
Click to expand...

Actually this is a factor key, because there is a way to know what's on your head if you see Black & White on B&C.
Also i can see that you're trying to solve this by using probability laws, and there is no way/solution for it using this method (Obviously they all have the same chance/probability of having a white or black hat if they see a 2 whites).
The trick is to assume you are one of them (let's say you're the winner) how could you guess your color is totally depending on why the 2 others couldn't guess theirs.
 
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they couldn't guess because they don't see 2 black hats, that's the only solution for instant answer
um, that implies, that if I see 2 white hats, and I don't wear black hat, I have white hat as well


DAMN!
 
HostMafia said:
spent last 15 minutes on this, and still no clue.

Alternative answer- since the prisoners can see each others hat, they are sitting in a circle, And one prisoner was able to see the reflection of his hat in the eye of other. (but i guess they are too far apart to do this :P ).


White hat , black hat , Is This SEO related question <!-- too tired to think -->
Click to expand...

ROFLLL :))
Just follow the clues bellow, the answer is very close.
 
Actually, it is what I said in the beginning, you didn't put riddle correctly, because, person B and C couldn't answer regardless of the hat I am wearing.
They could either see white black or white white. They didn't guess because it was not black black combination. So, if it wasn't black black, because they CAN see one white, and one X, regardless of which hat is on my head, no one is able to tell the correct answer, because there's possibility of both.

So, other 2 persons didn't saw black black, which doesn't tell which hat is on my head, because I know thy see one white hat.

The only logical solution is, that 2 persons could see same thing, or all 3 could see the same thing.
This doesn't give anyone advantage, to be the only one to give the proper answer.
 
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