Logic

[KoibitoKoi]

I found this one on another site.. see if you can grasp the logic behind the solution That's the more interesting part


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 . . ."

[netbattle]

I think you can't say it correctly without guessing. It could be both. Couldn't it?

[KoibitoKoi]

There's actually an answer to it and it's not 'both' or 'neither'

[Conjar]

The important information is that in the first few seconds all three wise men would know that there are more than one blue hat (if there were only one blue hat, one of the three wise men would see two white hats and straight away say that his hat was blue).

Now let assume that there are two blue hats and one white hat. In this case two wise men would see one hat of each colour and since they know that there cannot be only one blue hat they would quickly deduct that their hat is blue. But neither of them claims that his hat is blue, meaning that all wise sages see two blue hats.

Which leaves us with the only possible solution that all hats are blue, and our hero stood up and said: "The colour of the hat I am wearing is blue."

[Bam]

Originally Posted by Conjar

The important information is that in the first few seconds all three wise men would know that there are more than one blue hat (if there were only one blue hat, one of the three wise men would see two white hats and straight away say that his hat was blue).

Now let assume that there are two blue hats and one white hat. In this case two wise men would see one hat of each colour and since they know that there cannot be only one blue hat they would quickly deduct that their hat is blue. But neither of them claims that his hat is blue, meaning that all wise sages see two blue hats.

Which leaves us with the only possible solution that all hats are blue, and our hero stood up and said: "The colour of the hat I am wearing is blue."

Where does it state there can't be one blue hat? I thought he claimed the exact opposite of that.

[nhocpleiku]

blue hat is sure, ok?????????

[perces]

hrmm blue because if he was white, then the 1st sage would have stood up and claimed he was blue, since if the hero was white, and he was white, the 2nd sage would have stood up as he sees only 2 white hats making him the default blue. Since neither of the others stood up to proclaim there colours he defaults to blue. heres a lil graph.

sage 1 sees ethier BBx or BWB
sage 2 sees ethier BBx or BWB
hero sees BBB BBx

[Conjar]

Originally Posted by Bam

Where does it state there can't be one blue hat? I thought he claimed the exact opposite of that.

It states that there is At least one blue hat, but if there were only one the sage wearing it would see two white hats and authomatically realise that his hat is blue, and therefore straightaway say it. Since no sage claims it, all of them must see at least one blue hat, meaning that there must be more than one

[tou_c_vang22]

what's wrong with white hat they all the same hehehe jk

[aznangel]

oh i get it! they all struggled because they all saw 2 blue hats so the hats must all be blue...