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hard riddle- difficult to solve - need answers immediately

 
 
Reply Thu 26 Jan, 2006 01:42 pm
You are travelling in a deep, dark forest when, suddenly, on a dark and stormy night, you are captured by the kind-but-not-so-bright forest people. They keep looking at you and saying to each other, "It be a smart person!"

You are marched to their village and seated in the square. Before you are blindfolded, you notice two other lucky souls seated in chairs facing you. Then you are told that the forest people king is about to die. He previously sent messengers throughout the land seeking the 3 smartest people. You are one, and two others have also been found. He now gives you all a task to see which one is the wisest.

He tells you, "I have seated you in an equilateral triangle so that each of you faces the other two. 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, 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, (that's you!) say, "Your highness, I have a green dot. The reason I know this is that..."

How did you know?
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Lord Ellpus
 
  1  
Reply Thu 26 Jan, 2006 02:04 pm
...the hand that I've raised is holding a mirror?
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yitwail
 
  1  
Reply Thu 26 Jan, 2006 02:13 pm
hehe. since everyone raised their hand, everyone knows there's at most 1 red dot. and since i see that the others have green dots, i'm the only one who could have a red dot. so suppose i have a red dot. then the others would think, since there's at most 1 red dot, and i see a red dot, that means i have a green dot. and since everyone's smart, someone would tell the king rather quickly that he or she knows what color dot he or she has. but since there's a long pause, that means i have a green dot. Smile
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malik basha
 
  1  
Reply Thu 26 Jan, 2006 02:29 pm
can u explain me in a much clearer way
yitwail
 
  1  
Reply Thu 26 Jan, 2006 05:54 pm
yes, i you can tell me which part of my explanation is unclear.
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Ebuniagogo
 
  1  
Reply Sat 9 Apr, 2016 03:33 pm
@malik basha,

Since you see two green dots, you know at most there can only be one red dot. That red dot would be on your forehead, but it also could be a green dot at this point.
Now, here's the tricky part, and I'll do my best to explain it. The answer is in the fact that you have to now put yourself in to the mind of the other players. I'll label the two other players Player 1 and Player 2.
So step inside player one.
There are three options he can see.
Option 1. Two red dots
Option 2. Two green dots
Option 3. One red, one green
For option one to be valid you and player 2 need to both have red dots on your head. You can see that player 2 does not have a red dot on his head. So option 1 is impossible.
For option 2 to be valid you and player 2 need to both have green dots on your head. You see player two has a green dot, but you're unsure what you have. This option has the possibility of being true.
For option 3 to be valid you need to have a red dot on your head, since you see player 2 has a green dot.
So as of right now you are able to take out option one, and are only left with options 2 and 3. Here's the real meta part. Go back into player ones head. He doesn't know the answer. He's wondering if he has a red or green dot on his head.
So, Now compare what he's thinking to the options that are left.
Option 3- there is one red dot and one green dot. You would have the red dot, player 3 would have the green dot.
Compared with
Player one's uncertainty of having a red or green dot. If he had a red dot on his head, and you had a red dot on your head there would be two red dots. Since at the beginning we deduced that there could only be one red dot this makes option 3 invalid.
Option 2 is the only option left. YOU HAVE A MOTHER ******* GREEN DOT ON YOUR HEAD!!!!!! HOLLA!!!!

Love,
Ebuni
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