Riddle: Sages

[Lawnmooer]

"The colour of the hat I am wearing is..."

"Either blue or white."

 

[nondescript]

"not green."

If MY head were on the line, I would say that too.

This guy never said they couldn't take the hat off and look at it, or ask the other guys what color it is. Just that whoever answered first would win, and if you guessed wrong you died. Plus, he said that they would have A hat on their head, but had to guess the color of THEIR hat.

"The color these two see." (in case the hat on my head is my hat)
"the color this man says it is." (in same scenario)
"Blue, and it's on that man's head." <again, pointing at other sage's hat> (The scenario where the hat ISN'T the hat on my head.)

 

[MortyMnemonic]

I am going with White.

If each one of the other saw two white hats they would immerdiately called out "blue" but none of them did. That means they couldn't be sure they are wearing blue hats.
Therefore, the one who disturbs the "easy" solution for the others is the one who answers the riddle.

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.

Oh, shi- Didn't think of that. -.-

Well, nevermind.

 

[Crayzor]

Blue. Because no one else had stood up, meaning they all had to be blue?

 

[S.R.S.]

Doesn't he just walk out? Since it's should have been clear to him from the start.
If it took him this long to realise what hat he is wearing, then he doesn't deserve to be advisor.

Just saying.

 

[Celtic_Kerr]

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

This man is right, but the idea they were having was just "What colour is my hat"

It's the time that they sit and ponder it that gives it away.

If one person had a white hat, then the sage that saw one white and one blue would know that since there is ATLEAST one blue, the statistical odds were in his favour and they would not have sat down long.

Since they all had blue hats on, they all saw each other and saw two blue hats, and at that point it's all a question of whether they have a blue hat or a white hat. Since they were all so perplexed for so long, one sage realized the dilema and knew that his was blue.

 

[Celtic_Kerr]

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?

I also love your reasoning to this one

 

[Billion Backs]

Sounds like a bad way of choosing political advisers.

No wonder monarchy failed so hard, buncha inbred morons with overinflated self-importance and too much money that shouldn't really belong to them in the first place.

Also, blue, but it's a bit too late at this point.

 

[oktalist]

I have seen this puzzle elsewhere, called the "blue eyes" problem, done with 100 people with either blue or brown eyes on an island rather than 3 people with either blue or white hats in a royal chamber. It is a lot harder to figure out that way.

Bonus points if you can explain why it is neccessary for the king to tell them that at least one of them is wearing a blue hat, when all three of them can already see that that is the case.

 

[Celtic_Kerr]

I have seen this puzzle elsewhere, called the "blue eyes" problem, done with 100 people with either blue or brown eyes on an island rather than 3 people with either blue or white hats in a royal chamber. It is a lot harder to figure out that way.

Bonus points if you can explain why it is neccessary for the king to tell them that at least one of them is wearing a blue hat, when all three of them can already see that that is the case.

I believe this will answer your question

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 the smell of victory... And by victory, we mean Yahtzee's old socks!

 

[oktalist]

Alice sees that the hats of Bob and Charlie are both blue. Alice hypothesises that "if my hat were white, then Bob and Charlie would both see one blue hat and one white hat."

Alice further recognises that "if Bob saw one blue hat and one white hat, he would think 'if my hat is white then Charlie would see two white hats and know that his is blue, but Charlie hasn't said anything so my hat must be blue.'"

Alice concludes therefore, that because neither Bob nor Charlie has said anything, her hypothesis must be false; her hat can not be white, or one of the others would have realised that theirs was blue.

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.

That seems similar to what I said just there, but substituting the concept of fairness for the logical induction of the other sages' thoughts.

EDIT: Tweedpol and Chamale also got it.

Bonus points if you can explain why it is neccessary for the king to tell them that at least one of them is wearing a blue hat, when all three of them can already see that that is the case.

I believe this will answer your question

It didn't. In fact, it made the king's statement unneccessary. The answer is this:

Spoiler

Alice already knew that there was at least one blue hat. She already knew that Bob knew that there was at least one blue hat. But she didn't know whether Bob knew that Charlie knew that there was at least one blue hat.

Only when the king told them all that there was at least one blue hat, did Alice then know that Bob knew that Charlie knew that there was at least one blue hat, which she needed to know in order to apply the inductive process I described at the top of this post.

 

[tweedpol]

Ooh thought of a better answer:
He didn't say anything because herbs can't talk.