What is the answer to the riddle of the king and the three green dots?

[Toasthead]

WOuldnt it be as simple as if the one guy saw the two people with red dots had their hands raised his MUST be green?

--G

 

[Skyclad1uhm1]

Originally posted by: Toasthead
WOuldnt it be as simple as if the one guy saw the two people with red dots had their hands raised his MUST be green?

--G

Then each one would know it.

Btw, there is a flaw in the riddle. If someone only sees red dots he/she will not raise his/her hand, and will therefor not be able to lower it either. At least not in the way meant

 

[yruffostsif]

They should of played indian poker instead. I have the highest card!!

 

[Ynog]

Ok here is how I would have come up with the answer.

Ok.
All 3 people are suppose to be smart.

So now you have 3 green dots.

So when A looks at B and C he sees a 2 green dots. So he can raise his hand.
B does the same with A and C
and C does the same with A and B.

Now this is where you must think about your dot.

A must think, does he have or not have a red dot. Well A can see that B has a
green dot. Meaning that C will raise his hand not matter the color of A's dot.
A sees that C has a green dot so that no matter what color A's dot is B will raise his hand.

Now this will hold for each person A B or C. None of them will be able to tell the color of their dot.
However, if A had a red dot, then B and C would easily be able to tell that they have green dots.
And thus be able to answer the riddle. However since there is a long pause, that means no one can
answer the riddle, meaning A must have a green dot.

 

[BennyD]

there is a much easier way:

since the king said "As soon as you have figured out what color your own dot is, lower your hand" then they must all be green, otherwise the king would have given 1 person an unfair advantage because they would not be asked if they didn't have thier hand up in the first place.

 

[Titus_92]

The king is about to die and has no heirs to this throne. He sent messengers throughout the land seeking the 3 smartest people. The messengers return with three people. He now gives them all a task to see which one is the wisest.

He tells them, "I have seated you in an equilateral triangle so that each of you faces two others. While you are blindfolded I will paint a dot on each of your foreheads. Each dot will be red or green so that there can be any combination of red and green dots, for example, 1 red and 2 greens, or all red, etc. When I remove the blindfolds each of you must raise your hand if you see _any_ green dots, i.e. 1 or 2 dots. As soon as you have figured out what color your own dot is, lower your hand and tell me how you knew."

So he paints a green dot on all three foreheads. When the blindfolds are removed, all three hands go up. After a long pause, the wisest person says, "Your highness, I have a green dot." How did he know?

Proof by contradiction:

Assume the wise men are named A, B and C. A is the wisest.

A knows that B and C have green dots.
A assumes (for contradiction) that he has a red dot.

If this is the case, then B will see a green dot on C and a red dot on A.

B will also see that C has his hand up. If A is red and C has his hand up, this means that B must be green.

Therefore B will lower his hand after a short time.

But a long time has passed and B hasn't lowered his hand. Therefore A must be green.

We have assumed that A has a red dot and logically deduced a contradiction. Therefore our assumption is incorrect: A must have a green dot.

This is how A knows he has a green dot.

 

[SamQuint]

Okay, I think I got the answer:

This riddle can be proved by contradiction:

There are two cases when all 3 hands go up.
2G and 1R or 3G

Now assume that you have a red dot, also note that you see that the other two guys have green dots. In the case of 2G and 1R dot, either of the guys with the green dot will know immediately what color they have but the person with the red dot cannot know for certain what color they have. Since the two guys with the green dots do not know immediately what color dot they have, it contradicts the assumption that you have a red dot, therefore you have a green dot.

Yes this is right. Since there are only two situations where all three people raise their hands it is a matter of who figures it out the first. If I see one of the two others have a red dot, then I immediately know that mine is green because there would need to be two green dots. If I see two green dots then I think that if mine were red one of the other two would immediately know that they were the second green and they would drop their hand. Since neither immediately knew they were a second green by seeing one red then they all had to be green.

 

[Captante]

I'm thinking the king AND his freaking dots have been DEAD for nigh on 17 years now.... nothing left but the damn bones!