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  1. #1
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    Masters of Logic

    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?
    Trendem

  2. #2
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    Re: Masters of Logic

    Quote Originally Posted by Trendem View Post
    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?
    He knows the other two men have red dots on their foreheads. So instinct tells him to conclude that he must have a blue dot. However, he sees that each man is following the same assumption he is, IE, all three believe that since the other two have red dots on their foreheads, that he himself has a blue dot. So the man concludes that he must have a red dot on his forehead.
    But in your hearts revere Christ as Lord. Always be prepared to give an answer to everyone who asks you to give the reason for the hope that you have. But do this with gentleness and respect, keeping a clear conscience, so that those who speak maliciously against your good behavior in Christ may be ashamed of their slander.
    1 Peter 3:15-16

  3. #3
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    Re: Masters of Logic

    Quote Originally Posted by Mr. Hyde View Post
    He knows the other two men have red dots on their foreheads. So instinct tells him to conclude that he must have a blue dot. However, he sees that each man is following the same assumption he is, IE, all three believe that since the other two have red dots on their foreheads, that he himself has a blue dot. So the man concludes that he must have a red dot on his forehead.
    Wrong answer. Explanation of why your answer is wrong is below:
    1) The grand master did not say that there MUST be a blue dot. All three masters of logic are smart people, and are not given to unfounded assumptions. They know that it is entirely possible for there to be no blue dots at all.

    2) Even granting your assumption thingy, your answer still does not make sense. How did the man who guessed correctly "see that each man is following the same assumption he is"? There is no way the man can know what the other people are assuming.
    Also, if the other two men really assumed that they had a blue dot on their heads, they would have blurted it out. That they kept silent shows that they do not know what is the colour of the dot on their head.

    I must clarify, that the man who deduced that his forehead has a red dot, is CORRECT. So the question is how did the man arrive logically at this answer.
    Trendem

  4. #4
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    Re: Masters of Logic

    Quote Originally Posted by Trendem View Post
    2) Even granting your assumption thingy, your answer still does not make sense. How did the man who guessed correctly "see that each man is following the same assumption he is"? There is no way the man can know what the other people are assuming.
    Also, if the other two men really assumed that they had a blue dot on their heads, they would have blurted it out. That they kept silent shows that they do not know what is the colour of the dot on their head.[/SPOILER]
    I must clarify, that the man who deduced that his forehead has a red dot, is CORRECT. So the question is how did the man arrive logically at this answer.
    THen there's, I'm assuming, a number of ways to logically arrive at the conclusion. He could very well have taken it that, since the Grand Master painted two red dots, that he would have no reason to assume he had a blue dot anymore than he would have a red dot, and that it was a straight fifty/fifty guess.

    The room was dark and there's no indication that the Grand Master had two separate brushes or even that they could see whether or not there was even any blue paint at all.

    He felt his own forehead? If they had gone in and got painted and then left, he could easily just feel his forehead and see the paint on his fingers. That'd seem to be the simplest way to get a guaranteed answer. So I'll go with forehead touching.
    But in your hearts revere Christ as Lord. Always be prepared to give an answer to everyone who asks you to give the reason for the hope that you have. But do this with gentleness and respect, keeping a clear conscience, so that those who speak maliciously against your good behavior in Christ may be ashamed of their slander.
    1 Peter 3:15-16

  5. #5
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    Re: Masters of Logic

    Nope. The man who got the correct answer used logical deduction to solve the problem, not any guesswork or tricks.
    Trendem

  6. #6
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    Re: Masters of Logic

    Wise man 1 knows he either has a red dot or a blue dot. Looking around, he can see that all hands are raised, meaning that all 3 wise men see red dots. If wise man 1 had a blue dot, wise men 2 and 3 would see one red dot (each other's) and one blue dot (wise man 1's). As such, 2 or 3 would know that he a red dot because if he had blue, the other would see 2 blue dots and therefore not raise his hand. Because neither 2 or 3 say anything, wise man 1 can conclude that the dot on his head is red.

    "Opinion has caused more trouble on this little earth than plagues or earthquakes."

    ~ Voltaire ~

  7. #7
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    Re: Masters of Logic

    Absolutely correct, Voice. Here's the next one:

    The two losing masters wanted a rematch, so the grand master showed the three masters 5 hats, two white and three black. Then he said: "I will turn off the light and put a hat on each of your heads and hide the other hats. When I turn on the light you will have equal chances to win. Each of you will see the hats of the two others, however not his own. The first one saying the colour of his hat will win." Then before he could turn off the light, one of the masters (the same one again) guessed, what the colour of his hat will be.

    What hat was it and how did he know?
    Trendem

  8. #8
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    Re: Masters of Logic

    Because each wise man is to have “equal chances to win”, the master cannot place a white hat on any wise man’s head. If wise man 1 saw wise man 2 and 3 had white hats, he would know his was black (as there are only 2 white hats). If wise man 1 saw wise man 2 with white and 3 with black, he would know that 3 would either see 2 white hats (2’s and 1's) or one white (2’s) and one black (1’s). Because the former situation (2 white hats) is impossible, wise man 1 can conclude that the hat he will receive will be black (as will the other two wise men’s).



    "Opinion has caused more trouble on this little earth than plagues or earthquakes."

    ~ Voltaire ~

 

 

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