[rookie1ja]

Masters of Logic Puzzles II (hats) - Back to the Logic Puzzles
After losing the “Spot on the Forehead” contest, the two defeated Puzzle Masters complained that the winner had made a slight pause before raising his hand, thus derailing their deductive reasoning train of thought. And so the Grand Master vowed to set up a truly fair test to reveal the best logician amongst them. He showed the three men 5 hats – two white and three black. Then he turned off the lights in the room and put a hat on each Puzzle Master’s head. After that the old sage hid the remaining two hats, but before he could turn the lights on, one of the Masters, as chance would have it, the winner of the previous contest, announced the color of his hat. And he was right once again.
What color was his hat? What could have been his reasoning?

Spoiler for Solution:

Masters of Logic Puzzles II. (hats) - solution
The important thing in this riddle is that all masters had equal chances to win. If one of them had been given a black hat and the other white hats, the one with black hat would immediately have known his color (unlike the others). So 1 black and 2 white hats is not a fair distribution.
If there had been one white and two black hats distributed, then the two with black hats would have had advantage. They would have been able to see one black and one white hat and supposing they had been given white hat, then the one with black hat must at once react as in the previous situation. However, if he had remained silent, then the guys with black hats would have known that they wear black hats, whereas the one with white hat would have been forced to eternal thinking with no clear answer. So neither this is a fair situation.
That’s why the only way of giving each master an equal chance is to distribute hats of one color – so 3 black hats.
I hope this is clear enough.

Spoiler for old wording:

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?

[Rhyek]

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.

[larryhl]

Quote

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.

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.

[sharknateher]

I would suggest you rewrite the question because you state two masters want a rematch and that the grandmaster says I will place a hat on each of your heads (i.e. two) so because of this, white would be the right (equal) answer for two contestants. It is unclear in the setup that the grandmaster would also be wearing a hat.

[sk8erfou]

its imposible to accaully tell which hat would be placed on your head before it happened... the grandmaster could have made a mistake and placed 2 white hats and 1 black making it obviously and he just happened to guess the right answer and othe combinations... but the best adn quickest way would be to say

you are gunna place the white hat on me... then immediatly after go you are gunna place the black hat on me... making one of his statments right

[mrflax]

i had a slighly different approach using probabilities. Scenario 1: 2white,1black is agreed to be not equal for the 2 white. Scenario 2: 1white,2black; the person(pers1) who saw the other 2 black hats has a 66% prob. of knowing he has white. each of the persons(pers2&pers3) who saw 1white/1black also have a 66% prob. but of knowing they have black. The inequality here is that these people double there probability because they might be pers2 or pers3 each with a 66% prob. of knowing they have black. Therefore the only possible scenario would be Scenario 3: 3black hats! all 3 have 66% prob of knowing they have white. Would you agree???

[Riddari]

Quote

I would suggest you rewrite the question because you state two masters want a rematch and that the grandmaster says I will place a hat on each of your heads (i.e. two) so because of this, white would be the right (equal) answer for two contestants. It is unclear in the setup that the grandmaster would also be wearing a hat.

I agree the puzzle could be written better, but you still misinterpreted it. The "two losing masters wanted a riposte" against the winning master from a previous puzzle. The Grand Master has presumably already proven his superiority. I think it would be clearer to add the "against the winning master" to the puzzle as I did above. Then it should be more clear that there are three participants.

[Stickguy999]

black. it all has to do with probability

[harikrishna1985]

Cool!!

[mavedrive]

black.
losing gms: gm1, gm2
winning gm: gm3

case1: gm1 & gm2 wears white then left are blacks.
case2: gm1/2 is black, gm2/1 is white, gm3 is black-> left is 1black & 1white
--> from gm1 and gm2's point of view, they cannot tell. but from gm3,
since gm1 and gm2 cannot give the right answer, then he could tell that
he's wearing black. if he's wearing white, either of gm1/2 could have had
given the right answer... since gm1/2 did not answer, gm3 will know what
he's wearing.