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# Masters of Logic Puzzles I. (dots)

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Masters of Logic Puzzles I (dots) - Back to the Logic Puzzles

Three Masters of Logic wanted to find out who was the wisest amongst them. So they turned to their Grand Master, asking to resolve their dispute. “Easy,” the old sage said. "I will blindfold you and paint either red, or blue dot on each man’s forehead. When I take your blindfolds off, if you see at least one red dot, raise your hand. The one, who guesses the color of the dot on his forehead first, wins." And so it was said, and so it was done. The Grand Master blindfolded the three contestants and painted red dots on every one. When he took their blindfolds off, all three men raised their hands as the rules required, and sat in silence pondering. Finally, one of them said: "I have a red dot on my forehead."

How did he guess?

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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.

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?

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• 4 weeks later...
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...or he just looked into a mirror. ^^"

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• 1 month later...

Just a doubt:

the solution is based on the fact that the "wiser" is the "quicker" in finding the answer.

But the logic reasoning that the "wiser" uses, is actually based on the fact that the "less-wise" ones remains silent and so it implies that his dot (the wisest's) is red.

But if they could have remained silent for a certain amount of time even if his dot was blue.

As said, if everyone thinks at the same speed, they all should be saying "red". So if two are silent, doesn't actually imply mine is red, just they haven't yet realised.

To tell it in other words: if "C" had a blue dot, how long should he wait before knowing the answer? Suppose the other two are "slow", he would then say "red", which is wrong.

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• 2 weeks later...

I agree, the idea of the logical puzzle being based on knowing that the other guy should know what I think he knows I'm thinking is a little ungainly.

How about this: The grand master was also in the dark room when painting the three wise men, and yet they didn't hear him struggling to open a second can of paint in the dark, therefore only one collor was used, and once they were in the light and could see which color it was, the answer was apparent.

OR... As soon as the grand master painted the first dot, the wise man should've shouted 'Black!" since the room was dark, his spot would be black until such time as light fell apon it.

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There is a second, simpler solution.

It does not require the pause.

It is this:

The test is only fair if all three dots are the same colour.

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There is a second, simpler solution.

It does not require the pause.

It is this:

The test is only fair if all three dots are the same colour.

I like This solution. The Grand - Master would make it a fair test and the only way to make it fair is paint all 3 with the same colour. The best logician would deduce this and could shout his colour out in the darkened room.

The most devious of the 3 would touch the paint with his finger, while it is wet and and look at his finger in the light and see what colour is on his hand.

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There is a second, simpler solution.

It does not require the pause.

It is this:

The test is only fair if all three dots are the same colour.

I like This solution. The Grand - Master would make it a fair test and the only way to make it fair is paint all 3 with the same colour. The best logician would deduce this and could shout his colour out in the darkened room.

The most devious of the 3 would touch the paint with his finger, while it is wet and and look at his finger in the light and see what colour is on his hand.

yes - fair chances ... this one was meant to prepare you for the next puzzle - Masters of Logic Puzzles II. (hats)

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• 3 weeks later...

This is by far my favorite. My a-hole boss asked me this in junior high years ago. When I got it right, he said I had heard it before. And, by the by, in my opinion, logic puzzle solutions are about pure logic, not trickery.

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yep. i love these. there are so many variations, all are fun!

what would be funny is if the guy that yelled out "red!" actually had a blue dot, and another logician had already deduced that he himself had a red dot because he sees one blue and one red and the guy with red is raising his hand, meaning he sees ANOTHER red, which has to be the logician with red. But get this: what if that logician says nothing on purpose, so the logician with blue says "i know they're smart, they can quickly find out their own dots are red if mine was blue, but they are silent, so mine is red."

he shouts red and gets decapitated, and the other logicians grin cuz they hated him and were silent on purpose ;D

lol

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This is a quite easy puzzle and does not require any more solution.

However, we can abbreviate our thinking process thus:

All 3 hands went up, meaning there are at least 2 red dots.

If there was a 3rd blue dot, then 2 (each seeing a red and a blue) would immediately shout out the answer, "I have red dot" (logic: if I have also blue, all 3 hands would not go up, as the person with the red dot would see only blue; so I must have red dot).

But all were initially silent. So there is no 3rd blue dot. Therefore all must be red.

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ummm pretty simple one...ask one of the other two

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• 3 weeks later...

its not that hard.if they all have there hands raised then logically they all have red dots.

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• 3 weeks later...

you could not shout out your color in the dark room even if u were sure that the master was setting a fair test because you would not know if all the dots were red or if they were all blue until u saw the other 2.

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• 2 weeks later...

um. i feeling stupid.

couldn't I just ask one of the two others to turn around? if i see a hand in the air "RED" i would shout.

the other "wise" opinions cannot be concrete because they are all based on philosophy, not logic and therefore can be argued till the end of days ... but that's what philosophy is right?

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• 4 weeks later...

it is not mentioned in the puzzle all of them shud come out frm d room together.. if they are wiser .. first two will come out.... now u got what i mean to say..

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The correct answer is not a colour but this what colour is the dot on his own forehead because the grand master said "The one who says what colour is the dot on his own forehead first, wins" so therefore the grand master was the wisest among them just thought i'd point that out.

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• 2 weeks later...

Since blue is reflected more than red, all they had to do was lean the side of their head against the wall to see the reflection of either red or blue. Also, red paint is heaver than blue, so the guy could probably tell easily by its weight on his forehead--duh!

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Since blue is reflected more than red, all they had to do was lean the side of their head against the wall to see the reflection of either red or blue. Also, red paint is heaver than blue, so the guy could probably tell easily by its weight on his forehead--duh!

<!-- s:lol: --><!-- s:lol: --> very interesting ... so you could tell by the weight whether you would have blue or red paint on forehead

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• 3 weeks later...

what if one them being more wise realised that the one © who supposedly answered correctly, was basing his answer on the fact that the other two were staling and then in his wiseness witheld any answer and led (C ) to thinking he was correct and answer with the reasoning that the other did not know thus eliminating himself.

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Since blue is reflected more than red, all they had to do was lean the side of their head against the wall to see the reflection of either red or blue. Also, red paint is heaver than blue, so the guy could probably tell easily by its weight on his forehead--duh!

very interesting ... so you could tell by the weight whether you would have blue or red paint on forehead

you only have one dot on your head and therefore cannot compare the weights of the two , and cant conclude which is the heavier if you cannot compare them. interesting but wouldnt realy help you in this situation.

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what if the guy who said he has the dot first was colorblind?

he'd see the other two have the same dot color and would assume his would be different

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Maybe he just wiped his head and looked at his hand?

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• 3 weeks later...

I like this one.

The first answer works well - They are stated to be masters of logic - and all hands are raised so obviously anybody who can see a blue dot knows they have a red dot pretty quickly. Nobody does this so the next conclusion is nobody can see a blue dot.

But the second answer is much nicer - the grand master will design a fair test - clearly if the dots are different colours somebody has an advantage.

The nice thing about these solutions is that they don't conflict - but the time delay suggests that the first answer is the intended one.

JSL

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The man was Hindu.

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If one of them simply covered one of the others dots, he could immediately tell which color his was from the 3rd person because the only dot the third person would see was the first person's.

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