### Brain Teasers

# Three Sages

Once three sages decided to learn who of them is the smartest. So they went to the 4th sage and asked him to help them decide who is the smartest. The 4th one said, "I have five hats: two black and three white. Now I'll tie your eyes and put one of the hats on your heads. After that I'll untie your eyes and you will be able to see the hats of the other two sages, but you won't be able to see the hat on your head. And he who is able to state what color is the hat that is on his own head will be the smartest." After a while one of the sages told what color is the hat on his head.

How did he do that?

How did he do that?

### Hint

All of the sages had white hats.### Answer

Sage A thinks, "If sage B sees a black hat on my head he would think, 'if sage C sees that I and A, both have black hats, he would say that he has a white one. He didn't say that so I have a white one.' Sage B did not say that, so I have a white one!"Hide Hint Show Hint Hide Answer Show Answer

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## Comments

This is completely messed up, and its a copy of a very good puzzle which is also on this site which makes it worse. What happens if they are all given white hats?

How would that prove who is the smartest? A person can only answer depending on the situation, and on what hat they are wearing.

How would that prove who is the smartest? A person can only answer depending on the situation, and on what hat they are wearing.

i did not understand that what so ever it totally confused me

or maybe he saw teh other two had black hats?

I think that this is a pretty good teaser. I've heard it before a couple of different ways. It is still I think, one of the best puzzles. It takes a lot of thinking to find the solution.

that took a lot of thinking. I eventually got the explanation and now it makes sense. btw, cathalmccabe, they were all wearing white hats. if you really think about the explanation, it makes sense. it helps to draw a picture.

If you didn't look at the hint, Magmatt, your answer would've been perfectly fine.

well i was ok with the question...it was the explanation of the answer that totally got me. that confused me more than trying to figure out the annswer did....complete running in incoherent circles

i understood your explanation in the answer. it isn't that difficult, really, people.

it doesn't matter if it proves who is smarter or not that's not the teaser it's just an introduction.

smart teaser i liked it.

it doesn't matter if it proves who is smarter or not that's not the teaser it's just an introduction.

smart teaser i liked it.

May 08, 2006

There is only one absolute way to prove what color your hat is. If you see the other two are wearing the black hats, then you must have the white hat on. If both are wearing white there is still a white left and two black so you could be wearing either. Also if one is wearing white and one is wearing black again there is still both white and blacks out there that you could be wearing.

Tie your eyes? Ouch...

your answer only seems to make sense if there were only 3 hats in total but there are 5 in the question. i'm confused

If one of the sages sees the other two with black hats, they could assume that they have a white hat immediately. Since none of the sages said this, we know that only one black hat can possibly be out. After that, if one of the sages sees a white hat and a black hat, they would know that they have a white hat, but if they saw two white hats, they could not be able to figure out what color their hat was since there can either be one or zero black hats. Since none of them could tell what color their hat was, we can assume that none of the sages saw a white and a black hat. This means that all three hats are white. The answer was confusing, and it took me a while to understand, but the answer makes sense. Good teaser!

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