The Magic Wizard and three men - Solution
The wizard gave them 5 seconds, however, B only answered in the 4th second, which means that, the one on top of the stairs do not know the answer.
Being the one on top {A}, you are able too see all those below, {B and C} however, you still do not know the colour of your hat, this means that the colour of the hat of the man in the center and foot of the stairs {B and C} are different.
The man in the center {B}, must have thought of it and is very sure that the man in front of him had a hat of different colour, and since he could see the person in front, if the person in front had a white coloured hat, then his is black, or vice versa.
Sent in by Baldwin Kurniawan.
That is just a guess, there is no real answer.
If man A had a black hat, man B had a black hat, and man C had a white hat, his answer would have been incorrect.
Thus Man B only realized the color of his own hat, and that of man C and took a 50/50 guess about man A’s hat.
If the situation was that Man A could see B & C, man B could see A & C, and man C could see A & B, this would be different and no longer a guess. As it stands, this is no more a riddle than a true/false question that you do not know the answer to.
there’s no certainty to that answer. just because the person in front of him had black or white, does NOT mean he has a different color. that’s a stupid answer.
I could not understand the puzzle.
I’m not sure I understand.
You wrote:
“They were stationed in such a way that A can see B and C, and B can only see C, but can’t see A, and C can see none.”
but in the solution, it says, “The man in the center {B}, must have thought of it and is very sure that the man in front of him had a hat of different colour, and since he could see the person in front, if the person in front had a white coloured hat, then his is black, or vice versa.”
Does this mean B could see A?
“The man in the center {B}, must …and since he could see the person in front…”
Or does A know the color of his own hat?
Otherwise, B would see C’s hat color (let’s say black) but he wouldn’t know what color he himself was wearing. Finally, he realizes it must be white because A hasn’t called out the answer yet. But B doesn’t kmow what color A’s hat is, right? Therefore, even if he knows C’s color(black in this example) and even if he cam surmise that his is white(in this example) how can he know what color A’s hat is? A himself doesn’t know, correct?
So let’s say A has a white hat…
He still wouldn’t yell the answer, but B could surmise that he and C’s hat were different, but since B cannot see A, he doesn’t know if A’s hat is the same or different.
Is there a typo in the text copy, or am I looking at this wrong?
Thanks in advance. I am enjoying the site.
Okay, let’s think of this another way.
The three are standing in line front to back, facing the same direction. The person in the rear of the line can see the color of the hats on the heads in front of him and the person in the middle can see the hat in front to him. The person in the front doesn’t see any hats because, well, there are no hats in front of him.
Now, when the blindfolds are removed, the person in the back cannot answer because the there are two different colored hats in front of him. If they were the same color, he would have known he was the odd man out and would have answered by saying he was wearing the opposite colored hat. Since there was no answer from behind, the man in the middle realized his hat and the hat in front of him were not the same color and answered the question. It is not a guess or a 50/50 shot, his answer is 100% correct. Remember, only one man had to answer and answer correctly. It also didn’t matter what color hat man A had on his head.
Good puzzle!!
Thank you Randy for your keen use of logic! I would just like to add that in the question it said “there would be two hats of one color and one of another color”. So either two black and one white OR two white and one black. The answer is perfectly correct then. Neat puzzle!
B figured out his own hat color becuase A couldn’t answer
The only way A couldn’t figure out his own color would be if B and C have different colors. B realized this, and then guessed the opposite color from C’s hat.
Awesome puzzle, but think about this - B worked this out in 4 seconds and not only that, but worked out that A didn’t know and not that A was still thinking. For a man who was gonna be killed if wrong, he thought pretty quick!
Maybe it could be stated that the wizard asked “A” first and he couldn’t answer?
The riddle and the solution are sound, assuming all three men are reasonably intelligent.
Ok heres a little explanation….. Man A did not know the answer, so Man B could guess it.
Man A
If Man A saw both B and C and if B and C had the same colored hat, he woulda guessed his hat right, not wrong for clerafication. For him to have guessed it wrong, B and C had to have different colored hats.
Man B
Since, he got it wrong, Man B relized he and Man C had to have different hats for A to guess wrong. So, he guessed the opposite of C’s hat, since A got it wrong.
I hope my explanation has cleared things up.
it’s not stipulated in the problem that they can’t take off the hat and look??!!
Well, what I would do personally would be to just take off my headband and look. I mean, he never said not too…
Man A or B should have told man C what color hat C was wearing so that C could tell the wizard and they could go free!
Very good cause all they had to do was guess what color hate was on their head that moment. Confuse at first then understood it fine. Well Done!!
The riddle is absolutetly correct.
Man B based his answer on the fact that Man A could not answer. Man A would be able to answer only if B and C had the same color in which case he’d say the opposite of what he saw.
Man B concluded that Man A sees 2 hats of different color which meant that he is the opposite of what he saw infront of him
John you are stupid. Then is no guessing. Man B just realised that A doesn’t know then answer as he did not answer straight away. The only way A cannot know the answer is if he is seeing two different coloured hats, and B realises this is the case. B can see C’s hat and so knows he has the opposite colour. Okay I agree there is a bit of trust that B is putting in A but there really is know guessing.
its really a very good puzzle i properly understood this, n also found the same answer as given above….its really cool
I agree because if B and C had the same colour than A would have answered correctly within no time but if A does not answer or gets it worng than B must have a different colour to C.
This makes perfect sense.
First, let’s note that there are 3 caps. So that means either 2 are white and 1 black or 2 are black and 1 white.
A sees both B and C once the blindfold is removed. Because A does not know if there are two white or two black, seeing to different colored caps would make it impossible for him to determine the color of his own cap. B, who can only see C, recognizes A’s hesitation and realizes that his cap must be a different color from C’s, or A would’ve known instantly the color of his own cap.
Very clever.
The combination is of 2 white or 2 black.Since A could not answer B thought that his and the hat of C is of different color.Now the thing is that whatever be the color of the hat of C,B would assume the color of his hat is opposite.But he doesnt know the color of the hat of A,which maybe a black or white one.Since the combination is of 2 black or 2 white he had to take a guess..