BrainDen.com - Brain Teasers

# Masters of Logic Puzzles I. (dots)

## 58 posts in this topic

Guest

Lets say the people were A,B,C.Let C be the one who said that he had a red dot.Now the wise man had to paint at least two red dots else not all would have raised their hands.So he painted one red dot on A's and C's heads.Everyone saw at least 1 dot.C saw that A had red dot and B blue.He thought,"B is raising his hand cause he saw A.But A's also raising his hand so I must have a red dot"Note if all had ed dots nobody would be able to guess at all.

##### Share on other sites
Guest

if i were one of the three an i saw 2 people with red dots I would immediately know that I too had a red dot on my forhead because the wisest would have to be the one that realized he was being duped.

##### Share on other sites
Guest

It was painted on. No one said he couldn't touch it while it was still wet. The paint would have been on his finger

##### Share on other sites
Guest
Masters of Logic Puzzles I. (dots) - Back to the Logic Puzzles

Three masters of logic wanted to find out who was the wisest one. So they invited the grand master, who took them into a dark room and said: "I will paint each one of you a red or a blue dot on your forehead. When you walk out and you see at least one red point, raise your hands. The one who says what colour is the dot on his own forehead first, wins." Then he painted only red dots on every one. When they went out everybody had their hands up and after a while one of them said: "I have a red dot on my head."

How could he be so sure?

Masters of Logic Puzzles I. (dots) - solution

The wisest one must have thought like this:

I see all hands up and 2 red dots, so I can have either a blue or a red dot. If I had a blue one, the other 2 guys would see all hands up and one red and one blue dot. So they would have to think that if the second one of them (the other with red dot) sees the same blue dot, then he must see a red dot on the first one with red dot. However, they were both silent (and they are wise), so I have a red dot on my forehead.

HERE IS ANOTHER WAY TO EXPLAIN IT:

All three of us (A, B, and C (me)) see everyone's hand up, which means that everyone can see at least one red dot on someone's head. If C has a blue dot on his head then both A and B see three hands up, one red dot (the only way they can raise their hands), and one blue dot (on C's, my, head). Therefore, A and B would both think this way: if the other guys' hands are up, and I see one blue dot and one red dot, then the guy with the red dot must raise his hand because he sees a red dot somewhere, and that can only mean that he sees it on my head, which would mean that I have a red dot on my head. But neither A nor B say anything, which means that they cannot be so sure, as they would be if they saw a blue dot on my head. If they do not see a blue dot on my head, then they see a red dot. So I have a red dot on my forehead.

AND NOW I HAVE A HEADACHE!!!

##### Share on other sites
Guest

He just know from the other because the other two also raise up the hand

##### Share on other sites

There is something seriously erroneous in either this puzzle OR its answer.

1- In this puzzle:

In fact, if the Master really wanted to determine who the wisest one was using this experience, he had ONLY 2 choices to make:

A- All THREE should have RED dots

B- All THREE should have BLUE ones

He doesn't have any other choice!! Why?

Well simple: if he puts 2 RED and 1 BLUE or any other compbination, at least one of the "wise" men will be in a different situation than the others: it will either be easier or harder for him to know the answer, but NEVER THE SAME!

The initial conditions have to be the same for all of them so that the Master can compare their intelligence objectively and scientifically.

2- In the answer and its analysis:

The wisest man is simply the one who thought about the above analysis in 1, and predicted the master's choices. He will them shout out the same color that he sees on the others foreheads!

P.S: He doesn't even have to wait one second to do this!

##### Share on other sites
There is something seriously erroneous in either this puzzle OR its answer.

1- In this puzzle:

In fact, if the Master really wanted to determine who the wisest one was using this experience, he had ONLY 2 choices to make:

A- All THREE should have RED dots

B- All THREE should have BLUE ones

He doesn't have any other choice!! Why?

Well simple: if he puts 2 RED and 1 BLUE or any other compbination, at least one of the "wise" men will be in a different situation than the others: it will either be easier or harder for him to know the answer, but NEVER THE SAME!

The initial conditions have to be the same for all of them so that the Master can compare their intelligence objectively and scientifically.

2- In the answer and its analysis:

The wisest man is simply the one who thought about the above analysis in 1, and predicted the master's choices. He will them shout out the same color that he sees on the others foreheads!

P.S: He doesn't even have to wait one second to do this!

good point ... and that's exactly what happens in the next puzzle called Masters of Logic Puzzles II. (hats)

##### Share on other sites
Guest

i think its when the grand master said "when you see atleast one red dot raise you hand and say the colour of you dot on your head" since they all raised ther hand when the saw a red dot then they all had red dots, and one of them figured it out first

and they were looking at him

##### Share on other sites
i think its when the grand master said "when you see atleast one red dot raise you hand and say the colour of you dot on your head" since they all raised ther hand when the saw a red dot then they all had red dots, and one of them figured it out first

and they were looking at him

Not entirely correct.

Even if only two of them had red dots on their heads, they all would've raised their hands too...

##### Share on other sites
Guest

or mabey he notices that one of the other guys is looking at him when they raise their hand

##### Share on other sites
Guest

also he could of touched the paint with the back of his hand while it was still wet and when he raised his hand he saw the color, wise people know "if your not cheating, your not trying"

##### Share on other sites
Guest

I would agree they all must be red, that is why all hands were up and how he knew he had a red dot

##### Share on other sites
Guest

this was easy the reason he knew that he had the red dot was because he himself did not see any red dots. While the other two had seen a red dot on his head and put their hands up...duh!

##### Share on other sites
Guest
Masters of Logic Puzzles I. (dots) - Back to the Logic Puzzles

Three masters of logic wanted to find out who was the wisest one. So they invited the grand master, who took them into a dark room and said: "I will paint each one of you a red or a blue dot on your forehead. When you walk out and you see at least one red point, raise your hands. The one who says what colour is the dot on his own forehead first, wins." Then he painted only red dots on every one. When they went out everybody had their hands up and after a while one of them said: "I have a red dot on my head."

How could he be so sure?

Masters of Logic Puzzles I. (dots) - solution

The wisest one must have thought like this:

I see all hands up and 2 red dots, so I can have either a blue or a red dot. If I had a blue one, the other 2 guys would see all hands up and one red and one blue dot. So they would have to think that if the second one of them (the other with red dot) sees the same blue dot, then he must see a red dot on the first one with red dot. However, they were both silent (and they are wise), so I have a red dot on my forehead.

HERE IS ANOTHER WAY TO EXPLAIN IT:

All three of us (A, B, and C (me)) see everyone's hand up, which means that everyone can see at least one red dot on someone's head. If C has a blue dot on his head then both A and B see three hands up, one red dot (the only way they can raise their hands), and one blue dot (on C's, my, head). Therefore, A and B would both think this way: if the other guys' hands are up, and I see one blue dot and one red dot, then the guy with the red dot must raise his hand because he sees a red dot somewhere, and that can only mean that he sees it on my head, which would mean that I have a red dot on my head. But neither A nor B say anything, which means that they cannot be so sure, as they would be if they saw a blue dot on my head. If they do not see a blue dot on my head, then they see a red dot. So I have a red dot on my forehead.

I see it as this. he sees that all hands are up so there has got to be a red dot on his head but since they didnt talk he took advantage of this chance making him the wiser one. i know thats what you all said but i need to clear it up for myself.

##### Share on other sites
Guest
also he could of touched the paint with the back of his hand while it was still wet and when he raised his hand he saw the color, wise people know "if your not cheating, your not trying"

rofl thats hilariously awesome

##### Share on other sites
Guest
I see it as this. he sees that all hands are up so there has got to be a red dot on his head but since they didnt talk he took advantage of this chance making him the wiser one. i know thats what you all said but i need to clear it up for myself.

Remember, just because all hands are up does not mean everyone has a red dot on his head. Even if only two of them had red dots, all three would raise his hand because everyone would be able to see at least one red dot.

.....R

..R....B

Cover up any one of those three letters and you'll still see a R amongst the other two. The periods are just for spacing.

Edited by ALFRED

##### Share on other sites
Guest
Remember, just because all hands are up does not mean everyone has a red dot on his head. Even if only two of them had red dots, all three would raise his hand because everyone would be able to see at least one red dot.

.....R

..R....B

Cover up any one of those three letters and you'll still see a R amongst the other two. The periods are just for spacing.

I see where you're coming from on that and now that I think about it it makes sense.

##### Share on other sites
Guest

there may be two alternative ways of him knowing what color dot he had.

If he moves close to one of the others maybe he could see his reflection in their eyes.

he could also run around alot, get sweaty, and the color ink will start to drip

??

##### Share on other sites
Guest

the paint is still wet, he can touch his forehead and see which color he has... his hands are still up.

##### Share on other sites
Guest

Hey I have a more detailed version of the spoiler... it's forever long though.

I'll send it as an attatchment. Please read it, it took me like two hundred years to get everything the way I wanted it.

brain_teaser.doc

##### Share on other sites
Guest

Someone looked at him and raised their hand.

##### Share on other sites
Guest

There were two with red dots, one with a blue dot.

When the one who spoke up saw that the man with the red dot was raising his hand, he knew that his own dot must be red.

Otherwise, the other man with the red dot would not have raised his hand as he would have been looking at two blue dots.

##### Share on other sites
Guest

This is not a logic puzzle but a psychological one. There is no way to logically and with certainty determine what color the dot is. The answer is predicated on assumptions of the others' mental process. So perhaps it can be said that the winner is more 'clever' but he cannot be called the most logical.

##### Share on other sites
Guest

Guys are A, B, and C.... A would see red dots on B AND C... A would analyze as follows: when B raises his hand... he has to see at least on red dot... A and/or C and A knows C is red Likewise when C raises his hand... he sees A and/or B... and A knows B is red. .... but because all 3 raised their hands and nobody knows what their color is... then nobody saw a blue dot....

##### Share on other sites
Guest
The first one saying the colour of his hat will win.

White-black. No matter what color he gets, he said the color first. The Grandmaster never said "You only have one guess."