Author: docbill (Dr. Bill C. Riemers)
Date: 2004-Jan-17 17:37:22

Three men are discussing who is the smartest.  A woman tired of hearing the 
boasting, decides to try an intelligence test.

She blindfolds all three, and places them sitting in a circle facing each 
other.  She then paints a dot on the top of each one of thier heads.  
Finally she explains the rules.

When she counts to three all men will remove their blindfolds at the same 
time. The dot on their own head is either white or black.  If they see a 
white dot on either of the other two men they should raise their hands 
without delay.  The first person who correctly identifies the color of the 
dot on his own head and can state why is the smartest.

Before she can finish counting, Bob, the smartest man in the room correctly 
states the color of the dot on his head, and his reasoning.

What was the color, and how did Bob come to his conclusion?

                    Bill


Author: flint () Date: 2004-Jan-17 18:26:09 mmm.. I think I have it this time. Let's enumerate the possibilites: Dot sequence men_who_raise_hands w,w,w 1,2,3 w,w,b 1,2,3 w,b,w 1,2,3 b,w,w 1,2,3 w,b,b 2,3 b,w,b 1,3 b,b,w 1,2 b,b,b no-one raises hand When there are atleast two whites, atleast one of the men cannot be sure of his color (if all the three are white dots then none of the men can determine his color). Assuming the woman would consider being fair to all of them, she does not color more than two men in white. When exactly two of the colors are white, then the two men who see a black and a white will raise their hands. However, either one can deftly speak out the answer first (as black) before actually raising the hand, which again would be unfair for the man who sees both black and is depending on one or the other of the men to determine the color on his own head. This leaves the woman, in the interset of fairness, with the only option of coloring all three black. And thus, Bob could have answered before the count was over! (I hope a neophyte's inanities are forgiven on bboard. ":>) -F
Author: docbill (Dr. Bill C. Riemers) Date: 2004-Jan-17 19:26:48 You are getting close. Care to try again? Bill
Author: migo (Mikhael Goikhman) Date: 2004-Jan-17 19:39:11 I don't think I agree with your conclusion. :) It seems probable that the answer is symmetric, so noone benefits. Bob may think, if all colors are black, then noone raises the hand and all three know they have black points. So it is unlikely all three have black points. It is much more likely that all three have white points. So noone may immediately determine his color, but after some thoughts the smartest would determine his white color (because all others are silent). I would say that all colors are white. However we should not forget that the woman logic is in no way something deterministic, so any other answer may be correct as well. There is no enough information about the woman's mentality and intents. :) BTW, flint, you may depost your first 2 messages if you want. Press 'd 1.1' twice.
Author: flint () Date: 2004-Jan-17 20:05:06 Thanks migo for the help. Thinking about the puzzle, what is most surprising is the fact that Bob answers before the woman has finished counting. Hence his reasoning is entirely based on his pre-evaluated conjectures of the number of raised hands, which of cousre are inevitably based on assumptions about a woman's intellect and morality. While my sexist proclivity wanes in the pursuit of an intellectual train of thought, I should think that Bob was the smartest because he had bought out the answer well in time from the woman, possibly with an amorous foreplay leading to the pinnacle of .... ":> Am I going the right way, Bill? -F
Author: docbill (Dr. Bill C. Riemers) Date: 2004-Jan-18 00:31:22 Migo has it. Here is how it played out... ........ Jane counted, "One, two, ..." Before Jane could reach three, Bob interrupted, "I know the answer." Jane queried, "Perhaps you do not remember the rules? You need to know both the color of your dot, and provide a conclusive argument how you know it." "Well Jane," Bob began smuggly, "my dot is white. The reason is quite elementary. I only needed to know the rules, and that this was an intelligence to determine which of us is smartest. None of us would have agreed to this test if we doubted your abilities to prepare a worthy test. Hense I must conclude you painted my dot an all others the one color that would provide an intelligence test. "If you just wanted to be fair, you could have just given us all black dots. But then nobody would raise their hands. Anyone who didn't realize that ment we all had black dots would be an idiot. Ergo, that would not have been a intelligence test, but just a race to determine who could blurt out the answer quickest. "If instead you had given just one of us a white dot, the two of us with the black dots would raise our hands. The first to realize the person with the white dot was not going to raise his hand, would of course know the color of his own dot. That person would of course be the one with the white dot, since who else could know sooner that he did not intend to raise his hand. So again, this would not be an intelligence test, but the winner would be determined by who you placed the white dot on. "If instead you had given just one of us a black dot, everyone would have raised his hand. Either of the two people seeing a white dot would know the fact they raised their hands ment their own dot was black. Ergo, this would be a race between the two with black dots, and the man with the white dot could not prove his intelligence. "The only option left is to give us all white dots. In that case all of use would raise our hands. Only after one of us realized that the other two not blurting out the answer means his own dot must be black. This this was the only true option that could determine who was the smartest. "Having all reasoned this in advance, I knew I had to have a white dot on my head." Bob removes his blindfold and stares in disbelief at the two black dots on his friends heads. Everyone starts to laugh, except Bob. Jane chuckles, "Yes Bob, you are the smartest of all the men here, but you are also a fool. For only a fool draws a conclusion in the absense of empirical evidence. Your arrogance is your undoing, and irritates me endlessly. So I have proven once and for all that you are indeed the smartest of all the men in the room, but not the smartest person in the room." :) Bill
Author: migo (Mikhael Goikhman) Date: 2004-Jan-18 01:14:32 Yes, this is a nice story proving that women are the smartest among us in the sense of practicality. Are they also the smartest in the sense of pure (i.e. theoretical) intellect? No way, girls. However, Bill, did you copy and paste? You made 4 mistakes in 2 sentences where you call "black" color "white", and "white" color "black". I.e.: Either of the two people seeing a white dot would know the fact they raised their hands ment their own dot was black. Ergo, this would be a race between the two with black dots, and the man with the white dot could not prove his intelligence. should be: Either of the two people seeing a black dot would know the fact others raised their hands ment their own dot was white. Ergo, this would be a race between the two with white dots, and the man with the black dot could not prove his intelligence.
Author: docbill (Dr. Bill C. Riemers) Date: 2004-Jan-18 01:48:37 You got me there. I typed in the original problem wrong, as it was suppose to be they raise their hands if they see a black dot. So I had to reverse the answer. Obviously I missed a few spots. Bill