I feel the hat is white , as both are also seeing the hats as white and dosent have the courage to take a call. so better take the call and win before one of them do the same

If i am among those princes then my Hat's color would be white. WHY..?? I tell you

As two princes in front of me are wearing white hats.. And i could be any one of them. I could be first, second or third. And in all position it is only possible that two of infront of me wearing white hats , if all of us are wearing only White Hats.

If anyone sees two black hats, then he knows that his own hat is white. If any of the brothers sees two black hats, he would guess that his own hat is white and win the game. Now, suppose that you have a black hat. Each of your brothers sees 1 white and 1 black hat. They know that your hat is black. They also know that their other brother doesn't see two black hats (because no one has won the game yet). So, if you have on a black hat, that allows your brothers to figure out that their hat must be white. They didn't figure it out, so you must have on a white hat.

The other two brothers cannot answer because they can only see a white hat and a black/white hat (your hat). If there are 2 black hats in total and they can see a white and a black, they still wouldn't know what hat they have, and as there are 3 white hats in total, and the brothers see a 2 white hats, they still wouldn't be able to answer. Therefore there is no way you can know what hat is on your head.

LOL!!! this one is pretty good!! you just need to carefully anaylsis each case and theres also the hint in the question as well!!!

this is my answer:

GIVEN INFO:
- YOU are Prince A with either a BLACK or a WHITE hat
- Prince B has a WHITE hat
- Prince C has a WHITE hat

CASE 1:
- YOU have a WHITE hat
- Prince B has a WHITE hat
- Prince C has a WHITE hat

CONCLUSION FROM EVERYONE: no one can decide


CASE 2:
- YOU have a BLACK hat
- Prince B has a WHITE hat
- Prince C has a WHITE hat

Prince B's point of view:

I see one WHITE hat on Prince C and one BLACK hat on Prince A but I don't know my own hat, I have to think carefully

IF I have a BLACK hat THEN Prince C would immediately know he has a WHITE hat since theres only 2 BLACK hats, one on myself and the other on Prince A
BUT Prince C doesnt know! SO this would mean that I dont have a BLACK hat SO THIS MEANS I HAVE A WHITE HAT!!

I WIN!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
-----------------------------------------------

BUT CASE 2 didnt HAPPEN, NO ONE SAID ANYTHING, no one could decide

so the only Case that is acceptable is CASE 1 where EVERYONE has a WHITE hat!!!!!!!!!!!! =]

So whoever REALISES that CASE 2 cant happen and accepts CASE 1 would have guessed right! This is the hint from the question where the King said it was a Fair and Intelligent test, all 3 Princes had the WHITE hat which is fair and the first person to realise the scenario would be the most intelligent

ANSWER: YOU HAVE A WHITE HAT

hope this is not too confusing to understand =P

THE HAT IS BLACK COZ TWO OTHER SEE ONE BLACK AND ONE WHITE.THEY ARE CONFUSED.COZ IF THEY WOULD SEE TWO WHITE,IT WOULD BE EASY TO GUESS THAT THIRD IS ALSO WHITE BECAUSE KING CAN EITHER SELECT AT RANDOM OR CAN SELECT THREE WHITE.BUT NOW OTHER ARE NOT DARING TO EVEN GUESS THATS WHY I WILL SAY THE HAT IS BLACK.

If i were the prince i would wait till the other prince would guess because the King said he would kill the one that got it wrong so i would wait until one of the other princes got it right or died. Eventually i might have to guess

No woman is worth dying for, so I would just leave and settle down with some nice peasant girl whose family isn't so complicated.

The pince is seeing two white hats on other princes. Chances are that the king may have hidden one white hat and one black hat. And if a black hat is on somebody's head it is his! Also, others' inability points at their seeing one black hat and one white hat!!

just ask 'what color is my hat?', let the king know you know what color and then she decided on her own, but is it all worth it?????

the test can only be fair if all are wearing white hats...though I think I like Sam's answer better.

There is a problem. The question doesn't say *how* clever the princes are. You see, because everyone has a white hat the other princes should be able to guess what colour hat they have by using the same logic we are using. Because they dont, we don't know how clever they are, so the "prince B would figure out his hat if your's was black" argument is flawed, because we dont know if prince B is clever enough.

its white because the king said he would keep the game fair and there are 3 white hats for three princess

andria's got it.

It's been shown that no black hats were used, inasmuch as the king said this would be a fair test of intelligence. As has been pointed out, one could quickly deduce the color of his own hat if he saw even one other black hat. But here's where I think the problem twists around on itself. Of course the standard answer is that in consequence of there being no possible way the king could use black hats (the number is immaterial), there have to be three white hats. In such a case, you are said to be wearing a white hat. But as someone else pointed out, the instructions tell us the other princes are very intelligent men, which would mean that they should have come to the selfsame conclusion. To wit, they would know by the reasoning up to this point that they were wearing white hats. However, we are told that they remain silent. So, since they remain silent, the problem is flawed, or the other princes are less intelligent (and consequently, less trustworthy) than the problem suggests. Either way, we run into a problem with one of the premises of the riddle.

IT IS WHITE I AM WEARING ON MY HEAD....THERE IS LOGIC BEHIND IT....
SUPPOSE THE THREE PRINCES ARE A, B, AND C(ME).
HERE IF I ASSUME THAT I HAVE BLACK OVER MY HEAD THEN THE 2ND PRINCE B WAS ABLE TO COME OUT WITH THE ANSWER.

SO IT IS WHITE COLOR OVER MY HEAD WHICH KEPT CONFUSED THE OTHER PRINCES.

i feel the 'game' is not fair to everyone involved as mentioned as only one person can have a guranteed answer i.e if prince B saw a white and a black hat(black hat being my hat) then he would know that he cant have a black hat on due to the fact prince c would see 2 black hats and know its impossible that he has a black hat as there only is 2 black hats but its impossible for you to win as there is no guranteed soloution so therefore u having the disadvantage in the game

i thing this is not so hard l/k

Go into the room where the other 2 hats are and see the colours there...... then you know for sure what you got on your head!

because the king is fair to all of the three kings so he would but the three hats all over there heads so if i was the king i would choose white because he wouldn't give them two white hats and me a black one cause that wouldn't be fair.
My Answer is a WHITE HAT.

I would wait until the other 2 answered wrong and got killed and then i would get the princess! mwah ha ha ha!!!

just like I am confused, each other prince is. it can only be in a situation when everybody is at same level. HAT is white. its a "what other is thinking" test.

Timmy P is correct; if all 3 of us are wearing white hats, all 3 would know from the silence that all 3 of us are seeing 2 white hats and therefore all of us are wearing white hats. If the other two are not smart enough to immediately realize this, how can I be safe in assuming that they are smart enough to figure out what color their hat is if both are seeing one white hat and one black hat, the black hat being the one on my head? Or perhaps the other two hate me so much that even though they can see one white hat and one black hat and therefore know what color their own hat is they also know that if they remain silent I will guess (incorrectly) that I have on a white hat and will be executed for stating that I have on a white hat when I really have on a black hat. Are the other two devilishly clever or not as smart as the premise indicates?

if i see 2 white hats , and the other 2 princes can not tell what color hat is on their heads. that means they each see 1 white and 1 black. the only way they could know their color is if they see 2 blck hats. the answer is BLACK

Lets go through the possibilities.

A: B
B: W
C: B

A sees 1W/1B. Cannot decide.
B sees 2Blacks. Knows its white. C doesn't get a chance.

A: W
B: B
C: B

A sees 2 Blacks. Knows its white.

A: B
B: B
C: W

C Sees 2 black hats. Knows its white.

A: B
B: W
C: W
A sees 2 white hats. Cannot decide.
B: sees 1W/1B hat. Cannot decide.
C: Sees 1W/1B hat. Knows that A and B did NOT see 2 black hats. Thus has to be wearing white.

A: W
B: B
C: W

Same as above.

A: W
B: W
C: B

A sees 1W/1B. Cannot decide.
B sees 1W1/1B. Knows that he cannot be wearing black, or A would have known he wears white. Calls white.
C doesn't get a chance.


A: W
B: W
C: W
You are C.

A sees 2 white hats. Cannot decide.
B sees 2 white hats. Cannot decide.
C sees 2 white hats. Knows that neither A nor B saw a black hat, or they would have figured it out.


Do not try to prove that the hat is white. Prove that the hat is NOT black.

Oh, and I really dislike people who skirt logic problems with answers like, "How do I know that they aren't out to get me?" Thats not the purpose of the puzzle.

prince a sees white it couuld be both. if they each told the king ,p.a could hear,and find out.

Without a doubt that was how I figured this problem out. Took me about five minutes. Unfortunately there is no answer given, but this is the only one acceptable.

Does it say you can't look?? NO so look at your hat (it WILL be white)

Timmy P is correct. The puzzle should have mentioned that prices B and C were a just a little less intelligent than A OR something like they can navigate on X number of calculations in a logical tree.

The way the puzzle is stated implies that all prices are very intelligent and so they should all figure out what A figured out - that he has a white hat.

Considering that A, B and C are at same intelligence level, one solution or outcome if such a situation is simulated would be that all three prices wait / pause for some time and then shout at once "I have a white hat". OR another outcome would be that all three remain silent.

I think the problem is not with the puzzle but with the fact that it is very difficult to state this difference of prince A's extra intelligence (even if it might be just a bit more) compared to others in a language without giving out any clues or confusing the problem statement. [To make this clear assume that the problem does state that A is bit more intelligent than other. But we would not know how much more intelligent he is. So we would not know if B & C would even be able to make logical evaluation of "what-if" scenarios like suppose I (B) had a black ..then C will think about A and me (B) etc].

All in all it is a good puzzle BUT I think it will be a more challenging puzzle to fix the language of this puzzle and make it fool-proof.

My salute to anyone who could do that.

You see two white hats, therefore yours could be either colour.

From there perspective:

If yours is black, they see one black and one white. They know that theres is not black, as otherwise one of you would see two blacks, and now that yours is a white.

If yours is white, they see two white hats, and will not know either way which colour they are wearing, as it could be either. They know if they have a white one, others will see 2 whites, and not know either, and if he has a black, they see one of each colour, an d again will not know.

Therefore your hat MUST be white.

then again, if they were of equal intelligence, they would be able to use the same reason I applied above, by looking through the problem from yours and the other princes perspective.

and also, the King said its a fair test, and so as said above would not make it easier or harder for any one prince, so therefore must give all 3 the same colour hat.

You can prove your hat is white, but it doesn't explain the other princes reluctance to answer.

so overall... flawed puzzle.

You could side step the whole intellegence levels problem by having the King ask the Princes in order. That way the last prince asked, which would have to be you, would be able to answer. This does, however, make the test unfair to the first two asked.

go to the OTHER room where the king keep the OTHER hats

The king said he will kill the prince who was wrong , but also said that the test was fair and was a test of intelligence and bravery. So maybe the king is looking for the person who is intelligent and brave. That would mean he is looking for the person who realizes they will not be killed and steps forward first to answer. So basically the king is using scare tactics. That does not have anything to do with what hat you are wearing though. We know you could be wearing one of the two black hats or the last white hat. It could be the white hat because if all the princes are wearing white hats then say you are any one of the princes, you would see the other princes' hats and see they are white. That would cause you to think maybe you are the one with the different colored hat. This means the king would try and trick you. Also if you first look at the problem you would think your hat is black right away because the other princes' hats are white. There is a 50% chance you will get it right or wrong. There is no logical why to find the answer to this problem as many people probably know. This is one of those questions that confuses people with high IQ scores. IQ only tests how logicaly you think. Thise problem would be good for those out-of-the box thinkers.

well actually the king has been hired to kill you and tricks you into this game. you actually have a pink hat on your head and he is waiting behind you with a sharp axe. the other two guys are dressed up peasents paid to play the game so your gonna die if you guess and die of starvation if u wait. If you leave he will kill you when your back is turned dont play games like this children they only end up in tears...

In order for the test to truly be fair, each contestant MUST be given the same chance of winning, therefore must each have the same coloured hat--that can only be done with the three white hats.

white.

if anyone is having black hat other prince may guess right. because there is only 2 black hat and if two person are wearing black hat then 3rd can say his color.

I would tell the king "my hat is black" anyway we are going to died some day.

This was actually fairly easy and amusing. the problem doesn't say which prince you are. you could be Prince 1 (P1) or (P2) or (P3) either way, you see two white hats so no matter who you are/which prince you are, you have a white hat!

It's a fair game so

3 black hats = 60% of total hats
2 white hats = 40% "
5 hats = 100%

So,
Prince A = white hat (1/3 = 33,33%)
Prince B = white hat (1/3 = 33,33%)

If it's really fair, 3 hats split as:

60% white hats = 0,6 X 3 = 1,8 hats
40% black hats = 0,4 x 3 = 1,2 hts

The fact is tat I see 2 white hats. Really I asumed they are white. Really they are white only the part of the hats I can see from my position. I do not know what colour they are at the other side which I can't see.

Really, there is one entire white hat and the other is 80% white (the part of the hat I can see) and 20% black (hided to me)

Then, my hat must be entirely black to stand fair play.

Since none said their own hat was white, which is simple to find out as proven for many before me, the others are confused: A, wearing a 80% white hat sees one white hat and one black hat. B,wearing a 100% white hat, sees one black hat and the 80% white hat.

Option a): B sees in A his 20% black. Then he can reason the same way I've done and guess rightly his hat is white since mine is black.

Option b): B, as me, sees only the white part of the hat. If he hasn`t yet said anithing is because he hasn`t found out the statistical trick.

So

Prince C (me) = black hatand th winner takes it all

WHITE HAT! I figured it out since there was a similar puzzle to this, but worded slightly different.

the answer is obviously white and whats more is that the riddle doesnt tell us which prince we are so we could be one of the ones with a white hat and see 2 white hats, i must say this riddle is flawed

Does it say you can't ask someone what colour your hat is? I mean, everyone else's solution is smart and makes sense if you read it properly, but I look for simple solutions and loop holes and found that you could just ask for the answer. Sorry if that sounded COMPLETELY retarded.

well the colour of the hat is black,coz the princes are confused as they see two colours black and white and cant decide which colour they should say

The question is very simple.
A difficult ques. would have who is the most foolish among the 3 princess? (Assume princess to be numbered 1,2,3 and no. 1 prince is asked about his colour. Failing to say anything, prince 2 is asked and so on....)

For answer mail me mannharleen@gmail.com
Cheers.

I came to the conclusion that it was black based on two factors.

Factor number one, I treated this question similar to the Monty Hall question, although it only partially applies. I don't feel like explaining, so google 'Monty Hall problem'.

Factor number two came from the hint. They all have blind folds on, he can see the white through his black blindfold, but they can't see his hat through their blindfolds because the hat and blindfolds are both black. You can't see black through black, but you can see white through black.

His hat is black.

The question should at least mention that the Kind is wise and just, and that he is giving each of the prince's an equal change to solve the puzzle. Without that, your solution and reasoning is hog-wash.

It is definitely grey

verry nice...
the answer is white...
why?
suppose you are prince #1
1st clue-none of the two could answer...then they dont have 2 black hats...
2nd clue-if you have a black hat other prince #2 will think this way,
"if I have a black hat then prince #3 will say that he has a white hat,but he dont want to answer then I have a white hat!"

back to the first clue none of the two could answer then #1 dont have a black hat!!!
hence, #1 have a white hat...yeah!!!

one thing everyone has forgotten is that it says that the test is of intelligence AND bravery, and it says the other 2 princes are clever, but it doesnt say that they are brave. in that case, i think theyre all white hats and its up to the brave prince to step up and say his is white. THATS THE REAL TEST!

For being one of the easiest riddles this one has the most comments. Everyone in the first three answers got it right and there are still 50 comments to clairfy the thought process for the first 3 ??? All of you who commented after the first 3 went home without the princess because you took to long to think about it. LOL

If you read the question properly, it says the test is of "intelligence" AND "bravery". So if its just 3 white hats, its just a question of whose brave ?? So to be a question of intelligence, you need to be wearing a black hat. The question clearly says that the other two are not able to deduce the result. This is only possible if u r wearing a black hat, so the other two see 1 white and 1 black hat !! only u see two white hats and conclude yours has to be a black hat !!(since its a fair test of Intelligence too)

If a prince can see two white hats then he will be wondering why isnt anyone saying anything therefore he cannot be wearing a white hat because if he was then that would be all three whita hats and evryone would be able to see two white hats and they would all be thinking why isnt someone saying anything so he must be wearing a black hat so the others can see a white and a black in which case they cannot figure out their own colour hat but since he can see two white hats he has to be wearing black

Now, let us say i'm Prince-A, the other two princes are Prince-B and Prince-C.


When I'm having a black hat, then Prince-B will think like this - "Prince-C is keeping quiet just because he didn't see black hat on my head, else he would have shouted he has white hat. So that means I'm having a white hat". Immediately Prince-B will shout that he has a white hat. Prince-C will also think similarly. Now this didn't happen, since both Prince-B and Prince-C are still keeping quiet and unable to guess. So this "confusion state" will prevail among Prince-B and Prince-C only if I'm having a white hat (thereby not giving place for Prince-B and C to declare the hat they are wearing). So I should be wearing White hat.

it doesnt say that each prince has the same intelligiance and that is why you are the only one intelligent enought to work out your own hat is white therefore it isnt a "floor" in the puzzle its all of you not intelligent enough to read and understand what the puzzle is being said

some people are claiming there is no way to solve this because unless you see 2 black hats you cant figure out because if there are 1 black and 1 white or 2 white you don't know but it is not about what you know more about what your fellow princes don't know therefore you know! you see 2 white hats and know that your brothers see two white hats because if they saw 1 white and 1 black they would figure out theres is white because noone else knows and if theres was black someone would see 2 black so you know yours isn't black so it must be white!there you go :)

the hat is white because the other princes r intellegent and if eighter on saw 2 blacks they would know thier hat is white and if they saw one 1b/1w but no one told the king anything their hat would be white so if u had the black hstit would be an unfair selction and since the king promised it to be fair it would have to be a white hat

If the other two princes are soo smart, how come they couldn't deduce that their hat was white? They were all put in the exact same situation. LOL.
I'm only joking :S

I can see that many people (including me) have solved this problem. So either the princes weren`t smart at all, or the world is full of genii :)

If he's willing to answer when seeing 2 whites then presumealby the other 2 would also; therefore he has black.

Man, some people are really stupid. It took me a while to figure it out, and I had to draw pictures. So, one of the other princes probably would have beaten me to the punch. But I came up with the only answer a logical process can derive: white. The answer "black" can only come from fools who have various reasons (as opposed to the objective unity of logic) for their conclusions, all of them illogical and/or suffering from a failure to read the puzzle properly.

...For example, dojo, above, gets the logic precisely backwards. If hesitation results from seeing two white hats, then I can only be wearing a white hat, not a black one! Duh.

do the princes KNOW how extremly intelligent the other princes are? The only fact that is mentioned is that the princes know they are going to die if they give the wrong answer. So what if one of these smartasses is just paralysed with fear?

I would not dare to say:"The color is white".