Cunning Sage
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 . . ." (what colour is his hat? explain)
by world_pride
"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 . . ." (what colour is his hat? explain)
by world_pride
Labels: lateral thinking, logic, SharedPuzzle
posted by Mr Fahrenheit at
4:50 AM
14 Comments:
It's blue.
He's surrounded by mirrors, and by standing, he confirms this.
ok basically the sage realises that he has a blue hat, as the others have to the same look in their eyes [that being of seeing 2 other blue hates].
Its a probability problem, the possible combinations are:
B,B,B
B,B,W
B,W,B
W,B,B.
With those combinations he has a 75% chance of having a white hat on and only a 25% chance of having a blue hat on. So I say he has a white hat on.
its blue as he said their def wasn't 3 white ones
I guess he has a blue hat.
When sage A looks around he sees 2 blue hats. Then he starts to find out the others are thinking about.
If his hat is white: both sage B and sage C see a white and a blue hat.
Sage B, seeing a white and a blue hat must have started thinking: if his hat is white then there are 2 white and 1 blue hat. This way the one with the blue hat would have found out immediately that his hat is blue (because there must be at least 1 blue hat). But this didn't happen so sage B's hat can't be white. But he doesn't say anything so he doesn't see a white and a blue hat but 2 blue hats.
And that means sage A has a blue hat.
The answer is definately blue.
If SAGE A was white, then Sage B would see 1 white and 1 blue.
Sage B would think "if i'm white, then that would be 2 whites and Sage C would immedately know he was blue." Then he would know he was blue. But since he didn't, he must also see two blues.
Sage C would think exactly as Sage B.
Therefore, since no one said anything, they must assume that they all have blue hats.. Sage A was the first to figure the logic and speak "Blue!"
Since 1 sage saw two blue hats, then there may be 1 white hat, ro no white hats..
BBB or WBB
If there were only 1 white hat,
doh.. disregard the last few lines after the big space in my post above.. still had text off the bottom of the screen i didn't see..
BLUE!
If B,W,W the person wearing B would instantly know they were B since there cannot be 3 W.
If B,B,W one of the people wearing B would know they were B after a few minutes because if they were W (B,W,W) it would have been over immediately, see above.
With these two cases in mind, the only way everyone could be stumped was if they were all BLUE!
I think you're right. The mirror thing would have been kind of cheap, but you never know with these riddles.
This is a simple case. Any sage would be able to eventually figure out. The mind of the other 2 sages were "blind folded", due to the stress caused by being afraid of behead...
In other words, this #1 sage has fast mind, therefore, more intelligent than others.
Dremer, I do have a problem about the title. #1 sage was not "Cunning" at all... How about "Shrewd"? Shark
the answer as most of you have guesed is blue. and the riddle has no mirrors in it.(:S). but it was about how fast the sages figured out that both of his rivals had that question in their eyes. is there 2 blus or 2 blus and 1 white?.
SHOOP DA WOOP IMA FIRIN MAH LAZER
I give you alot of credit world_pride I love your riddles. but his one has alot of loopholes.
From the clues left ther is still a fifty fifty chance that he either has a blue or white hat.
Sage A (the guesser)
Sage B (Blue)
Sage C (Blue)
Sage A sees two blue hats. So he can either have a blue or white
Sage B sees either two blues or one blue and one white. Begin trying to figure out if he has a blue or white hat
Sage C sees the same as sage B
As far as thinking the same thing they all want to know what color hat they have on. That is what is in quotes just paraphrased alittle.
Oh, it is a fifty fifty chance of either hats
"kaim 381": you may have your final say, if you were right.
Unfotunately, it is not. Pls read
what "Sage Ano 6/9 10:18a" said.
""
IF Sage A had white hat, then Sage B would see 1 Blue and 1 White.
Sage C would also see 1 Blue and 1 White.
Sage B would then figure:
"If I had a white, then Sage C would see 2 Whites."
"In which case, Sage C would have immediatedly announced that C himself has Blue.", which did not happen.
Therefore, Sage B did not see 1 Blue and 1 Whte.
In other words, Sage B has seen 2 Blues.
This proved that Sage A has Blue, indeed.
""
It is NOT 50-50 guess. It is 100% correct logic. It is trying to put your feet into others' shoes. Then you see the truth out of it.
Shark.
it all.
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