[wolfgang]

A King have 3 sons, he make no difference between them, he told them that the one who is most clever than the other two brothers will be the next king.He showed them five feathers (2 of them white color and three black).

He asked them to sit in a triangle ( each one can see the other two).he put the feathers in a sac,then he attached a black feather to the hat of each one.each one now can see two black feathers but he don`t know which color he had.

the king asked the 1st one what feather he had.....he said ..I don`t know.

the 2nd also said...I don`t know.

the 3rd one said...I must have a black feather!!...how did he know? and why was he very sure?

[Guest]

The first one thought that it wouldn't be fair if there are 2 white and 1 black since the one with the black will see two whites and instantly know his colour. He also knew that if there is 1 white and 2 blacks the first black will see a white and a black, since 2 whites and a black won't be fair he couldn't have another white and that tells him that his colour is black. That won't be fair as well, which leaves the only fair distribution - 3 blacks

[bonanova]

the king asked the 1st one what feather he had.....he said ..I don`t know.

the 2nd also said...I don`t know.

the 3rd one said...I must have a black feather!!...how did he know? and why was he very sure?

Anyone who sees two whites knows he is black.

1 didn't know his own color, so 1 didn't see two whites.

3 reasons that if 3 were white, 2 would know that 1's uncertainty meant 2 was black.

Since both 1 and 2 were uncertain, 3 knows that 3 is black.

[Guest]

By the way a similar version was posted before Anyway, nice puzzle.

EDIT: Nice way of thinking Bonanova

Edited October 13, 2010 by kristmark1

[Guest]

Well bonanova's answer is good as long as the first two guy's are dickheads. If they were clever they would see that there is unlikely to be enough info to be sure but if they honestly answer then they are supplying brother three with valuable clues and thus giving him the crown!

No, the first brother wants a shot at the title and doesn't want the other two assholes to swindle him out of a cushy job with a huge harem (or at least a bunch of mistresses)

So brother 1 is more likely to take a shot and guess a color, as he may jag it and be right and this will also potentially throw a spanner in the works for the other slobs. This would also give him some wriggle room later if he is wrong to argue that even if he got it wrong wrong he is still more clever than the others who simply tried to logic it out or guess instead of using logic and cunning.

If brother two was switched on he would figure that brother one is a sneaky SOB and ignore brother ones answer and have a crack at the crown himself with a guess. If he goes with black he could come up with a convincing speel why this is so and still be in with a shot at the crown even if he is wrong.

By the time we get to brother three, who knows his brothers are all crooks, he would have no use from the first two guesses and would have to try bullsh*t his dad about how he's the clever one without relying on his guess or hints from his brothers, so i say he cannot be very sure at all.

[Guest]

The clue was at the beginning. The king treated each of them with no difference, hence if one had black they all would have black.

[bonanova]

Well bonanova's answer is good as long as the first two guy's are dickheads. If they were clever they would see that there is unlikely to be enough info to be sure but if they honestly answer then they are supplying brother three with valuable clues and thus giving him the crown!

No, the first brother wants a shot at the title and doesn't want the other two assholes to swindle him out of a cushy job with a huge harem (or at least a bunch of mistresses)

So brother 1 is more likely to take a shot and guess a color, as he may jag it and be right and this will also potentially throw a spanner in the works for the other slobs. This would also give him some wriggle room later if he is wrong to argue that even if he got it wrong wrong he is still more clever than the others who simply tried to logic it out or guess instead of using logic and cunning.

If brother two was switched on he would figure that brother one is a sneaky SOB and ignore brother ones answer and have a crack at the crown himself with a guess. If he goes with black he could come up with a convincing speel why this is so and still be in with a shot at the crown even if he is wrong.

By the time we get to brother three, who knows his brothers are all crooks, he would have no use from the first two guesses and would have to try bullsh*t his dad about how he's the clever one without relying on his guess or hints from his brothers, so i say he cannot be very sure at all.

Hi knob, and welcome to the Den.

The solution you suggested doesn't respond to the question that was asked. You missed the point.

So here's a hint: Often, how a puzzle is worded - what it says and what it doesn't say - will provide a clue to the correct answer, which might be only one among many otherwise possible answers. Your post raised a lot of interesting possibilities. Like the character of the sons and of the King, and whether certain derogatory adjectives may or may not have applied to them as people. The clue here to finding the correct answer is to see precisely what was asked. The Original Post [OP for short] gives us what happened. What the King said, and how all three sons answered. What it did not say was that they were stupid, underhanded, liars, or anything else related to their character. So to add those possibilities makes it a different puzzle. The general rule is to take the OP as stated. Nobody was said to have made a guess. Or lie saying they didn't know when in fact they did. Rather, all three were asked to say whether they knew the color of their feathers. Their answers were No, No and Yes.

The question then was how the third son could know, when the first two did not.

Here's another hint. No one here is impressed with offensive characterizations. Whether they're applied to the puzzle makers, the characters in their puzzles or the Brainden members who post their solutions. I'm going to assume you were just having some good fun and hope you stay around. Cuz you clearly know how to think out of the box, and that's a plus. But I think you'll enjoy your membership here a little more, and certainly for a longer period of time, if you're thoughtful in choosing the boxes that you go outside of.

Word to the wise.

[bonanova]

The clue was at the beginning. The king treated each of them with no difference, hence if one had black they all would have black.

First, the question wasn't what color were the feathers.

The question was how did the third know when the first two did not.

That solution you give does not answer that.

But leave that point aside. Let's say the King made it clear to the sons that he

was treating them all alike. Well, in that case the first son would say black.

But is that really treating them all alike? No. Why? Read on.

By controlling the order in which his sons spoke, the King did not treat them all alike.

If equal treatment is invoked to make all the feathers black, then the first to be questioned would say his was black.

If it is not invoked, the first two to be asked were ruled out because they could not know.

Under either assumption, the King chose his successor by choosing the order of questioning.

To make it entirely impartial, the King would give them all black feathers and say to them all,

The first to tell me the color of his feather, and the reasoning by which he knows he is correct,

that is, not just a lucky guess, that son will be my successor.

Then they would all sit in silence until one did the reasoning that the silence of the other two

proved his feather was black. The first son to do that would have proved to be the most clever.

But ... that wasn't what was asked. And equal treatment isn't what happened.

[Guest]

i don't see why his feather can't be white.

if the first person saw black and white he has no way of telling his own color.

same for the second person.when it gets to the third person and he sees two black, why would his feather necessarily be black?

by saying "i don't know" the only info you are conveying is you don't see two white feathers.

you can still see one.

[Guest]

Hello, new to the forum, but I've been following for a few weeks, courtesy of iGoogle.

#2 can reason as follows: if #3 was white, then I would know that I am black, because I know that #1 cannot see two whites. Unfortunately, I can see that #3 is black, and I don't know whether #1 can see 0 or 1 whites, so I don't know my colour.

#3 can reason as follows:

I know that #2 would know that he was black if I was white (by the reasoning in the 1st sentance above). Therefore, because #2 did not know his colour, I am black.

Edited October 14, 2010 by Peter Jackson

[wolfgang]

Hi knob, and welcome to the Den.

The solution you suggested doesn't respond to the question that was asked. You missed the point.

So here's a hint: Often, how a puzzle is worded - what it says and what it doesn't say - will provide a clue to the correct answer, which might be only one among many otherwise possible answers. Your post raised a lot of interesting possibilities. Like the character of the sons and of the King, and whether certain derogatory adjectives may or may not have applied to them as people. The clue here to finding the correct answer is to see precisely what was asked. The Original Post [OP for short] gives us what happened. What the King said, and how all three sons answered. What it did not say was that they were stupid, underhanded, liars, or anything else related to their character. So to add those possibilities makes it a different puzzle. The general rule is to take the OP as stated. Nobody was said to have made a guess. Or lie saying they didn't know when in fact they did. Rather, all three were asked to say whether they knew the color of their feathers. Their answers were No, No and Yes.

The question then was how the third son could know, when the first two did not.

Here's another hint. No one here is impressed with offensive characterizations. Whether they're applied to the puzzle makers, the characters in their puzzles or the Brainden members who post their solutions. I'm going to assume you were just having some good fun and hope you stay around. Cuz you clearly know how to think out of the box, and that's a plus. But I think you'll enjoy your membership here a little more, and certainly for a longer period of time, if you're thoughtful in choosing the boxes that you go outside of.

Word to the wise.

Hi...I am so glad to see so much replies....anyhow...the 3rd son was to say the same answer even if he didn`know what the other two brothers said !

[k-man]

i don't see why his feather can't be white.

if the first person saw black and white he has no way of telling his own color.

same for the second person.when it gets to the third person and he sees two black, why would his feather necessarily be black?

by saying "i don't know" the only info you are conveying is you don't see two white feathers.

you can still see one.

Suppose I have a white feather. Then both my brothers see one white and one black feather. The first one doesn't know his color, so the second brother must be thinking "If my feather was white then the first brother would see 2 white feathers and would know for sure that his feather is black, but since he doesn't know, it means my feather is black". So if my feather was white the second brother would know for sure that his feather is black. He doesn't know, so my feather must be black.

[wolfgang]

Hello, new to the forum, but I've been following for a few weeks, courtesy of iGoogle.

#2 can reason as follows: if #3 was white, then I would know that I am black, because I know that #1 cannot see two whites. Unfortunately, I can see that #3 is black, and I don't know whether #1 can see 0 or 1 whites, so I don't know my colour.

#3 can reason as follows:

I know that #2 would know that he was black if I was white (by the reasoning in the 1st sentance above). Therefore, because #2 did not know his colour, I am black.

great..... respect!!

[Guest]

A saw something else than "2 whites" (if he did, he would win) - so he was unsure of his color.

B was unsure because of A's reply as well as he saw 2 blacks himself. Had he seen white on C, he would have guess his black.

C knew for sure, if he was wearing white, B would have told his color correctly. Since he failed, C was sure that his color was black.

C knew the other two wearing black

However i think the king was insane to put his sons on this test. C's position had big advantage of hearing what the other two had to say. However, A,B might be really stupid to "pass on" rather than to guess, when throne was on stake