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 color 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 color of my hat?"
For what seemed like hours no one spoke. Finally he stood up and said, "The color of the hat I am wearing is . . ."
What did he say, and why?
Originally posted by apathistI am wearing a blue hat.
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 ...[text shortened]... he stood up and said, "The color of the hat I am wearing is . . ."
What did he say, and why?
The choice for the Person is bbb or wbb.
If he wore a White hat the choice for his opponents would be wbb and wwb. Since www is explicitely not the case one of the Opponents would realize that he can't wear a White hat since the other did not claim wwb. So he can't wear a White hat himself.
Originally posted by PonderableThat's the part I have trouble wrapping my head around. The indecision of the others turns out to be a source of information. Let's hope I guess that the other two wisest men in the land didn't come from a shallow pool.
... one of the Opponents would realize that he can't wear a White hat since the other did not claim wwb. ...
Originally posted by apathistThe Point is:
That's the part I have trouble wrapping my head around. The indecision of the others turns out to be a source of information. Let's hope I guess that the other two wisest men in the land didn't come from a shallow pool.
If I see two White hats I know that I have to wear a blue one since the combination www is explicitely excluded. (combination wwb).
So if I see one white hat and one blue hat, the guy wearing the blue hat would be the one seeing two White hats (and claiming the win) if I wore a White hat. If he does not Claim the win I am not wearing a White hat, so I wear a blue hat.
So if I see two blue hats and nobody is claiming the win. I have to wear a blue hat.
The Point is to react slow enough to give the others reason to Claim thier win (if any) and to Claim the win before them 🙂.
btw: since seeing White hats gives a clue, the fairest Option for the King would be to give each one a blue hat to give equal chances...