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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 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.

makes sense when u think about it

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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 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.

much simpler!!

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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

yes but if you have blue on you head you wont see it will you? i believe that it is a matter of patience, the one who is the most patient will not walk away after a while and then the wiser sees that the other still raises his hand but the fairer solution is also very good

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I had a more linguistic answer; the other two were women "wise masters" were women.

Since the grand master said, "The one who says what colour is the dot on his own forehead first, wins," and the problem ends with, "How could he be so sure?" I thought it was on of those lateral thinking questions which assaults the assumption of gender archetypes.

When I saw the length of the solution (only a glimpse) I figured my solution wasn't the right one ...so I'll keep at it.

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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.

you cant see the other logicans in the darkroom and looking at your finger would be cheating.

look at their eyes and if they look at you and put their hand up then you have a red dot

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just say both colors before the other two say anything

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What if one, taking advantage of the fact that he knew that if only one dot was red, the bearer of that dot is bound to lose, eliminating that possibility, and knowing that all dots must red, came out with his eyes closed, and, after a pause, opened them to see both opponents with their hands in the air before announcing that his one was...That would eliminate the possibility of the others deducting the answer first. This would be wise, but only if all dots weren't blue. In any fair scenario the answer would be based on the speed of reaction of each man. The grand master would only have thought up the longest scenario.

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i got it i think.....there are 3 ppl and so one of them will have a blue dot.......therefore the third person must have either a red or a blue dot.....this means that one of the three people will be seeing two ppl with the same colour....and since according to the question the person shouts out red it means that the other two had blue dots on their forehead and so he had to have the red dot....THIS SOLUTION IS VALID ONLY IF ALL THREE DOTS ARE NOT OF THE SAME COLOUR.