Riddle: Sages

[Celtic_Kerr]

The three wisest sages in the land were brought before the king to see which of them were worthy to become the king's advisor. After passing many tests of cunning and invention, they were pitted against each other in a final battle of the wits.

Led blind-folded into a small room, the sages were seated around a small wooden table as the king described the test for them.

"Upon each of your heads I have placed a hat. Now you are either wearing a blue hat or a white hat. All I will tell you is this- at least one of you is wearing a blue hat. There may be only one blue hat and two white hats, there may be two blue hats and one white hat, or there may be three blue hats. But you may be certain that there are not three white hats."

"I will shortly remove your blind folds, and the test will begin. The first to correctly announce the colour of his hat shall be my advisor. Be warned however, he who guesses wrongly shall be beheaded. If not one of you answers within the hour, you will be sent home and I will seek elsewhere for wisdom."

With that, the king uncovered the sages' eyes and sat in the corner and waited. One sage looked around and saw that his competitors each were wearing blue hats. From the look in their eyes he could see their thoughts were the same as his, "What is the colour of my hat?"

For what seemed like hours no one spoke. Finally he stood up and said, "The colour of the hat I am wearing is . . ."

 

[Celtic_Kerr]

Oh, and I'll give a hint after an hour if no one guesses it by then

 

[Grouchy Imp_v1legacy]

"not green."

Sorry for the low-content post, but that's all I've got. It's been a long day and I'm not firing on all cylinders.

 

[zombiejoe]

ON FIRE! HELP ME!

*Idk*

 

[Bobic]

Blue, if he could tell the other sage's were having the same thoughts as him then they were also seeing a 2 sages wearing blue hats (i'm aware it probably wasn't meant in this way but with riddles you never know)

 

[HSIAMetalKing]

[font color=blue]Riddle me this, riddle me that~[/font]

 

[zombiejoe]

Blue, if he could tell the other sage's were having the same thoughts as him then they were also seeing a 2 sages wearing blue hats (i'm aware it probably wasn't meant in this way but with riddles you never know)

I'm going to go with this guys hat idea

 

[comadorcrack]

He should look up

 

[Silent observer]

Blue, if he could tell the other sage's were having the same thoughts as him then they were also seeing a 2 sages wearing blue hats (i'm aware it probably wasn't meant in this way but with riddles you never know)

YOU SNEAKY NINJA!

 

[wfpdk]

he should just ask the other sages what color his hat is.

 

[The Ambrosian]

I'm just confused. I'm saying blue but It can't be that easy cuz that's a one in two chance.

EDIT: what the ninja said.

 

[dfcrackhead]

Blue, if he could tell the other sage's were having the same thoughts as him then they were also seeing a 2 sages wearing blue hats (i'm aware it probably wasn't meant in this way but with riddles you never know)

I vote this.

 

[tweedpol]

There cannot be 2 white hats since if there were one sage would have quickly guessed himself blue. There cannot be 1 white hat since that would make one of the others see the white hat wearer and think 'if i were wearing a white hat the blue guy would have guessed by now, therefore i'm blue' therefore there can only be blue hats since no one has answered.

 

[Robert632]

Purple. He was a very suicidel sage.

O.T:I'm just going to go with what this person put. It's about the only thing that makes sense, unless the clue you will give us in an hour tells us differently.

Blue, if he could tell the other sage's were having the same thoughts as him then they were also seeing a 2 sages wearing blue hats (i'm aware it probably wasn't meant in this way but with riddles you never know)

 

[Piflik]

Blue...any other possibility is unfair...if two had a white head, the third would know his is blue...if one has a white hat, both the others would know their's were blue (since 1 blue would be unfair)...this leaves three blue hats as the only fair posiibility and since the King would like to have the best choice, he wouldn't make an unfair bet.

What did I win?

 

[PoliceBox63]

There cannot be 2 white hats since if there were one sage would have quickly guessed himself blue. There cannot be 1 white hat since that would make one of the others see the white hat wearer and think 'if i were wearing a white hat the blue guy would have guessed by now, therefore i'm blue' therefore there can only be blue hats since no one has answered.

you win, I'd say

 

[Chamale]

I'll try doing this by going into the minds of the other sages. Sage A is "our" sage, while sages B and C are the ones known to have blue hats.

Hypothetically, suppose A has a white hat. B and C see this, and they might be wearing blue or white hats as far as they know. But if B sees a white hat on A's head, then he starts to wonder. If B had a white hat, then C could easily deduce that C has a blue hat. Since C does not quickly make this guess, B knows that B's hat is blue - but he could only deduce this is A's hat is white. Since no one spoke for a long time, apparently sage A's hat is not white, since someone else would have worked out the colour of their own hat if A had a white hat.

So sage A, "our" sage, is wearing a blue hat.

Edit: Dammit, I'm ninja'd. I started before anyone else used this line of reasoning, I swear.

 

[Grouchy Imp_v1legacy]

Hang on, the king never said the sages couldn't take their hats off. So surely, one of them just took off their hat, looked at the damn thing, and said what colour it was?

 

[Wrists]

If he saw two white hats, he could say with certainty that his is blue. Since they say nothing he has several options, if neither sage says anything then it is safe to say that they have figured out that they do not have a white hat on. If one sage saw a white and a blue but have noticed that the other sages have said nothing then we can assume that he knows he does not have a white hat because the sage who can see two colours would have said they had blue. Because neither of the other sages have reached this conclusion, he must be wearing a blue hat, as this creates a stalemate in that none of the sages knows what hat they can be wearing.

I apologise if this explanation is a bit scattered, it made sense in my head.

 

[tweedpol]

Blue...any other possibility is unfair...if two had a white head, the third would know his is blue...if one has a white hat, both the others would know their's were blue (since 1 blue would be unfair)...this leaves three blue hats as the only fair posiibility and since the King would like to have the best choice, he wouldn't make an unfair bet.

What did I win?

You win a humiliating defeat at my hands *possibly premature victory dance* -You know my name...- fear the goat in the hat!
I'm not sure fairness comes into it, it's more that if there were any white hats someone would have guessed quickly.

EDIT: I'm suddenly very aware i got this first by being on the escapist at half 4 on a beautiful summer's day... I swear I'd only been on 5 mins! I had other internet related stuff to do... ahem.