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Masters of Logic Puzzles II. (hats)


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37 replies to this topic

#21 tehpengywin

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Posted 10 December 2007 - 09:37 PM

If 2 dudes were wearing white hats then the dude with the black hat would know he had a black hat so it wouldn't be fair. So he knew they would all have black hats to make it fair. Simple. But I don't get the question...the way I see it there's 2 dudes and the grandmaster so wheres the third dude coming from......
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#22 taqasim

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Posted 11 December 2007 - 06:21 AM

The Grand Master plus three wizards. They're like his students, and he's the teacher giving them a test. The Grand Master is not participating as a test-taker, he's only there to judge. He probably wears a hat, but it's not part of the contest. It wasn't stated clearly in the original riddle. Of the three student-wizards, there is clearly one who is the star pupil. Get it?
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#23 stupidamerican

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Posted 12 February 2008 - 01:12 AM

Because the problem is to say which color will be on your head (is on ur head), wouldn't it be best just to blurt out "Black!! White!!" very quickly?
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#24 anand

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Posted 18 February 2008 - 03:59 PM

It is black. The solution is simple.

GM1, GM2 and GM3

First I am considering GM1 is the one who answered the question.

2 white/ 1 black

If GM1 and GM2 is wearing white GM3 would have immediately given the answer and if GM1 and GM3 is wearing white then GM2 would have responded, both GM2 and GM3 are quiet so this possibility is ruled out.

2 black/white

Case 1: GM2 looking at GM1 and GM3

if GM1 is black and GM3 is wearing white (or vice-versa) immediately GM2 would have said he is wearing black, because if GM2 is wearing white one of the other two would have immediately answered.

Case 2: GM3 looking at GM1 and GM2 - same as above

if GM1 is black and GM2 is wearing white (or vice-versa) immediately GM3 would have said he is wearing black, because if GM3 is wearing white one of the other two would have immediately answered.

Since GM2 and GM3 haven't answered yet which means GM2 (GM1 and GM3) and GM3 (GM1 and GM2) are looking at 2 black hats so for sure GM1 must be black.

So GM1 comes with an answer Black.
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#25 sunshipballoons

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Posted 03 March 2008 - 07:55 PM

The question is ambiguous to some extent, but at least it makes the essential point that the contestants answer by shouting out their answer. If the contestants were instead asked to write down their answers, each would have an equal chance of getting it right if all 3 hats were black, or if there were 2 black and one white hats.
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#26 Naruto Uzumaki

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Posted 05 March 2008 - 05:31 PM

I’d submit the correct color is white since it was the only color to choose from. Scientifically, white is the reflection of all colors in the spectrum while black is the absence of color.

We're not talking scientifically, we're talking about the chances of the hat's options <_<
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#27 Naruto Uzumaki

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Posted 05 March 2008 - 05:32 PM

The Grand Master plus three wizards. They're like his students, and he's the teacher giving them a test. The Grand Master is not participating as a test-taker, he's only there to judge. He probably wears a hat, but it's not part of the contest. It wasn't stated clearly in the original riddle. Of the three student-wizards, there is clearly one who is the star pupil. Get it?

no :huh:
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#28 TOPHAT

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Posted 25 March 2008 - 06:19 PM

Black, 3 masters and three black hats
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#29 bobbyb

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Posted 14 April 2008 - 07:07 AM

The way i read it was that the GM was testing the two failed masters with a task that he thought was so daunting that if either of them got it right, it would dethrone him as GM. (ie. if either of them got it right, they would become GM. so, two masters, two hats with two black and three white.)

if your opponent was wearing a black hat you would have a 75% chance that you were wearing a white hat.
if your opponent was wearing a white hat then you would only have a 50% chance then you were wearing either color.

the logical choice would be to jump the gun and assume that you would be wearing a white hat.
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#30 Ony

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Posted 15 April 2008 - 08:05 PM

The way i read it was that the GM was testing the two failed masters with a task that he thought was so daunting that if either of them got it right, it would dethrone him as GM. (ie. if either of them got it right, they would become GM. so, two masters, two hats with two black and three white.)
--if your opponent was wearing a black hat you would have a 75% chance that you were wearing a white hat.
--if your opponent was wearing a white hat then you would only have a 50% chance then you were wearing either color.
the logical choice would be to jump the gun and assume that you would be wearing a white hat.

That was what I thought too, but my friend pointed out that it said "Each of you will see the hats of the two others, however not his own"
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