Brain Teaser ;)

[eLiu]

ok...here we go:

In ancient times, four mathematicians discovered this game of logic. The four men were Hermos, Xentos, Appino, and Tenedos. Hermos seated the other three men, one behind the other, so that Xentos saw Appino, and Tenedos, and Appino saw only Tenedos. Tenedos, who was in front, saw neither Appino or Xentos.

Hermos had five hats which he showed to the three men. Three of the hats were gray, and the other two were white. Then Hermos put a hat on each man and tossed the remaing two aside.

"What color is your hat Xentos?" asked Hermos. Xentos did not know, Appino did not know the color of his hat either when asked.

Tenedos, who could not see any hats at all, gave the right answer when he was asked the color of his hat. What was the color of his hat? How did he figure it out?

edit: i don't know what the answer is

-eric

 

[NDGeist]

grey... i feel smart. i tried this riddle a year ago and couldnt get it... but right now i got it


easy... if xentos didnt know... then the 2 hats in front of him were not BOTH white.. because otherwise his would be grey. henceforth, either one or both of of the front 2 have grey hats... if appino looked forward and saw a white hat, he would have to be grey and he would know... but he looked forwared and saw a grey hat.. so he isnt sure if he has a grey hat... TEnedo's knows that he has a grey hat because the other 2 arent sure...

edit, more readable

 

[eLiu]

oohhh....lol that's right

hehe

 

[rangeLife]

NDGeist: if apino looks forward and sees a white hat, how does he know he has a grey hat? arent there two white hats? how does he know he's not wearing a white hat as well?

 

[viewton]

<< NDGeist: if apino looks forward and sees a white hat, how does he know he has a grey hat? arent there two white hats? how does he know he's not wearing a white hat as well? >>



that's what I was going to ask....

 

[eLiu]

If they were both wearing white, Xentos would know he has a gray one--there are only two white hats.

 

[viewton]

i understand now..tricky!

 

[NDGeist]

w00t!

 

[darkjester]

It's like this...

(I'll refer to the men by the first letter of their name --ie, H,X,A, and T.)

You have to look at the combinations and what could have happened. Tenedos thought the following:

Let say that A and T had white hats. Well, then X MUST have a grey hat, and he would have been able to answer that he had a grey hat. But he didn't answer, so either A and T had conflicting color hats (white and grey or vice versa) or they both had grey hats.

But then when A was asked, he would have thought:
Since X didn't know, A and T must not both have white hats.

If T had a white hat, then A could have answered grey, because otherwise X would have known. But A didn't answer, so T &quot;must be wearing a grey hat because that's the only way A could have a white or grey hat and not know which it is.

So Tenedos, thinking all this, busts out with a great big old &quot;My hat is GREY, Hermos, you crazy old coot!&quot;

Enjoy!

 

[Mithras]

The whole riddle hinges on the fact that each one knows that the ones behind him are very wise. So Apino knows that the guy behind him did not see 2 white hats. Or something like that

 

[darkjester]

Wow, in the time it took me to type that up, all you guys answered. When I started to type, no one had answered it yet.

Kudos to us all.

 

[YisSerL]

Ah...a classicial example of mathematical induction!

 

[darkjester]

<< Ah...a classicial example of mathematical induction! >>



I wouldn't really call this mathematical induction. In mathematical induction, you prove something is true for any k, and then subsequently prove it's true for k+1. So if P is true for 1, then it's true for 2. Since it's true for 2, it's true for 3. ...ad infinitum.

This is more like logical deduction.

 

[TechaNAN]

barf

 

[nd]

Not too hard, simple logic answers this. The only catch is you have to make the assumption that the participants themselves are logical and would be able to figure out their color if they had enough facts.