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# Masters of Logic Puzzles II. (hats)

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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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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

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Black, 3 masters and three black hats

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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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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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sorry but i dont see the part where you stated there was 3 masters.. im lost

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that's an incorrect statement. if you said light instead of color, that would be right. black is the absence of light, while white is the aggregation of all light in the spectrum. however, when talking about colors, white and black are both valid colors.

makes sense to me

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Posted · Report post

I like this one alot. I said black for a reason similar to that, but I didn't think it out as thoroughly as it is explained. I'm going to try this one on my friends.

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sorry but i dont see the part where you stated there was 3 masters.. im lost

This problem is a continuation of another one. In the first one it lists the Masters.

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Masters of Logic Puzzles II. (hats) - Back to the Logic Puzzles

The two losing masters wanted a riposte (Edit: against the winning master), so the grand master showed them 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?

I got black because if he knew the light would be turned off then the color of his own hat, regardless of if it was black or white, would be black.

Even if he got a white hat i figure that it would be black when the light was turned off.

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WOW.... some people think too much...

the simplist solution is that there are 3 "logic master" who will be tested and in order to make the test fair to all they have to have the same color hat (or dot) and therefore they will need to have black hats as there are only two white ones...

on another note...

yes, black is the absense of all light and white is the combination of all light in the spectrum. when you are talking about "color" it is exactly the oposite. black is made up of all colors and white is then the absense of color. either way this does not matter in the least. just because the lights are off in a room does not change the chemical make up of an object and the objects will retain their color. if you close your eyes it doesnt change the fact that the grass is green. if the sun were to burn out and all light in the world went out, my eyes would still be blue, my hair still blond and there would still be two white hats and three black hats!

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The olny thing i can think of is the master is thinking he will get a black hat because there are more, so that would be the most likely one to get, would it not?

<_<

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The official answer is actually logical and can work, but I think I have an even better one.

Unfortunately "ThunderChicken" already have said the answer I've thought of, but I'll explain more clearly.

The winning master of the previous contest is obviously a bit of a wise-a** (like philosophy masters out to be); so he decided not to wait for the master to turn on the light and to use the situation to his advantage.

The Grand Master had turned the lights off and unless given otherwise – it was pitch-black to our concern. In full darkness all the hats are black, even if they're white with the lights on.

Now if you think I'm a bit of a wise-a**… then first of all… you're right. Second – here's the scientific answer – Color of an object is the way we perceive light determined by its frequency which is determined by the way light interacts with the object. So!... when there's no light – there's no color... there's only black.

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