Video

It does indeed simplify the problem. It also sucks the mystery and delight out of the problem. If there are 3 men and I know one of the hats is red, then if I see only black hats on others, don't bother raising hands. My hat must be the red one.

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For clarity it should say, "WHEN I was two years old..." just saying 😃

exactly

No. The statement is, “you’re either wearing a red or black hat.” Doesn’t mean any one of the mean has to be wearing a red hat.

​@@I_need_a_new_user_name Exactly <"each is wearing EITHER a black hat or red hat">

@cjmacq-vg8um <"A hat is placed on each man's head. Each is told you have EITHER a black hat or a red hat">. Key word EITHER

The person giving the test did not say one has a red hat. He said EITHER one has a red hat OR they all have black hats. Its one of the three guys that ASSUMED there should be one red hat. He assumed wrong.

The flaw here is that the smartest guy would reason his hat is black because if it was red, then the other two would have answered with no pause. The very assumption relies on the reason the other two paused or not paused. But if the other two don't reason the same at the same time, that assumption becomes unreliable. If they were not smart enough to reason their own hat is black at the same time as our smartest guy, then they may pause even if they see a red hat or may answer quickly even if they see two black hats. The smartest guy would still interpret the assumption and reason similarly but his answer would be wrong.

The employer would not have chosen the one red hat scenario because it would be unfair to the red hat candidate. Why eliminate potentially the best candidate for no reason.

@@42976675 That's all you learned from my comment? That's not the point. You wouldn't hire the guy who answered his hat color quickly but gave a flawed reason. Why conduct the test for no reason.

there's a flaw in this test. the person giving the test is lying when he says one of them has a red hat. that means to get the correct answer those taking the test must assume they're being lied to. no one would assume that because there's no reason to assume it. what the employer is actually saying is - the first applicant that deduces the employer is lying to them gets the job. what kind of way is that to run a business?

@@cjmacq-vg8um No, each person is simply told they either have a black or a red hat. They might assume there is at least one of each color, but they are never told that.

@@ThePopeII ... with the mere mention of a red hat people are going to assume there's a red hat in the mix. the test is purposely misleading. its what's known as a classic "trick question." there's many ways to reword the test so its clear there maybe no red hat at all. sorry, i think the logic and the test are flawed.

@@cjmacq-vg8um Yea I agree that makes the puzzle extra tricky. It can vary a bit depending on how the instructions are given. However it could still be seen as a test to see how well people pay attention to detail for the specific instructions given, as well as having the reasoning ability to solve it.

@@ThePopeII ... we also have to remember this was a thought experiment. it was never actually used by any employer to determin someone's employment. could you imagine if we had to start solving silly riddles and puzzles to get a job? this particular puzzle reminded me of those yt "i. q. tests" that contain nothing but trick questions, riddles and puzzles to solve. this was an interesting puzzle i was destined to fail because i'm TOO logical!

What???. The problem said 3. I Don't get the job because if one has a red hat he sees 2 black hats but it's if you see a black hat. So, if one has a red hat they all 3 still rase their hands. So, one with a red hat still rases his hand.

@@davidheathcoat3408 Maybe I didn't explain it well. Lets accept the 3 men, 3 black hat solution of the video. In a group of 3 men where they each see black hats on the other 2 and all 3 raise their hands, THEN blessed with perfect logic, each of them should conclude that their own hat is black and each should race to give the correct answer. NOW, introduce a 4th man who thinks, I see 3 black hats. If my hat is red, then I don't matter to the other 3 men and they should STILL find the correct answer with their perfect logic. But none of them are speaking up. It can ONLY be that my hat is NOT red, so my hat MUST be black and I shall give it as the correct answer.

@@pascal1947 It wouldn't work with 4 men because if your hat were the only red hate, each of the other 3 men would see 2 black hats. So they would not know their own hat was black, because the other two men wearing black hats would be seeing each other's black hat.

there's a flaw in this test. the person giving the test is lying when he says one of them has a red hat. that means to get the correct answer those taking the test must assume they're being lied to. no one would assume that because there's no reason to assume it. what the employer is actually saying is - the first applicant that deduces the employer is lying to them gets the job. what kind of way is that to run a business?

​@cjmacq-vg8um they did not say there was a red hat. Either means maybe. Each of you will either have a black or red. Not one of you will have a red hat.

there's a flaw in this test. the person giving the test is lying when he says one of them has a red hat. that means to get the correct answer those taking the test must assume they're being lied to. no one would assume that because there's no reason to assume it. what the employer is actually saying is - the first applicant that deduces the employer is lying to them gets the job. what kind of way is that to run a business?

Thank's, that' what I was gonna say!

The explanation of "there was a pause then the man knew his hat was black" is correct. However, they would all know this, not just one of them.

Very simply...a very-much dumbed-down, classless audience.

De-evolution.

Even if the person has a black or red all three see a black hat and if there is a red hat they still lift the hat.

Agreed.

But the other two men would reason exactly the same as the first guy and thus all conclude their hat is black simultaneously. Because if you otherwise assume the other two men are less intelligent, then you couldn't assume the reason why they would (or would not) answer. You can't assume they'd be smart enough to recognize they don't immediately know that they have a black hat and not smart enough to draw the same conclusion as the first guy to deduce that they do have a black hat.

@@packerfan2010 No, the idea is to determine who is the smartest. Assuming one guy is smarter than the other two, he's the one who will first figure out that his hat must be black.

@@kenhaley4 you should read reply then because if only one was smart enough to deduce his own hat is black and the other two couldnt then his rationale is flawwed because its based on assuming the other two are smart enough to respond or not respond when they did If you assume only one of the three guys is smart enough to figure out his own hat color and the other two are not, you create a paradox because the reasoning that would lead the smart guy to his conclusion relies on the other two to be equally smart but you're assuming otherwise, completing the contradiction

​@@packerfan2010 Let me reiterate. Assume I'm one of these guys, and I know the other two aren't stupid. After all, we're all applying for the same job. So, I look at the others and see 2 black hats. Now I think, either my hat is red or black. If my hat is red, each of the other guys sees one red and one black hat. We all raised our hands, so they know we all see at least one black hat. It would only take them a few seconds to realize they're looking at each other's hat, and they would almost immediately announce that their hat is black. But several seconds go by, and no one says anything. So I conclude, they must not see a red and a black hat. They must be looking at 2 black hats, the same as me. Therefore my hat must be black. Now, sooner or later, we can assume all 3 guys would reach the same conclusion, but the smartest guy would reach that conclusion first. It wouldn't be simultaneous, because it's not an easy conclusion to arrive at. This is a classic problem--I first heard it decades ago.

@@kenhaley4 The difference between the first guy answering and the third guy answering would only be a few seconds but you're just splitting hairs at that point.

Turns out there wasn’t any red hat.

No, to demonstrate the logic of the problem you need to have everyone wearing black hats or two wear black and one wear red hat. 0 black and 3 red: no hands raised 1 black and 2 red: two hands raised 2 black and 1 red: three hands raised 3 black and 0 red: three hands raised The solution is obvious and immediate if you see 0 or 2 hands raised so you need 3 hands raised to figure the logic of the problem.

@@packerfan2010 Your delineation is correct which illustrates the problem's problematic issue.

@@roseymalino9855 The problem's problematic issue is not the necessity of Prescence of each color, which is your assertion. My replied proved that's not the case.

Actually, the first one to realize that none of them can answer, and also realize why- understands that his own hat is black.

@@peterbaruxis2511 your flaw is assuming only one can draw that conclusion. The rationale for one getting it correct fails if the other two dont also get it correct You can't assume the other two are smart enough to know their hat cannot be red while also assuming they aren't smart enough to know that their hat must then be black

False, two black hats and one red hat would cause three hands to raise.

Never ever ever assume for a logic problem that just because the question/problem/riddle exists that it must be difficult.

@@packerfan2010 yes but the answer would be immediately obvious to the people with black hats

Your first paragraph is false. No matter if all 3 have black hats or one has a red hat they all SEE A BLACK HAT....so the guy that says his hat is black has a 50/50 chance..the instructions are not giving enough info to do anything but guess. Now if the instructions say IF YOU SEE 2 BLACK HATS RAISE YOUR HAND THEN THERE IS ENOUGH INFORMATION TO BE 100%. SO, IF I SAID I HAVE A BLACK HAT THE CORRECT ANSWER IS I HAVE A 50% CHANCE OF GETTING IT RIGHT. BECAUSE IF I HAVE A RED HAT BOTH THE OTHER GUYS SILL RAISE THEIR HAND. 50% GUESS. THEIR IS NO 100% ANSWER SO NO CORRECT ANSWER.

YES! Exactly! Someone gets it!

The all black hat scenario is the only equal opportunity scenario which is the only one the employer would use to find the best applicant. But might find three.

One was just a bit more intelligent than the others? Sigh…

@@gravizfake In that case, no information infered from their actions is reliable so he was only correct by luck.

So, there's some element of timing because he said PAUSE and its bascially process of elimination. The guy who answered correctly eliminated every other possibility. If you were one of the three guys and saw two black hats, there's two possibilities. Either your hat is red or its black. Suppose your hat is red. Let B and C be the other two guys. B raises his hand because he see's a black hat on C's head. C only sees a black hat and a red hat but because B raised his hand, C knows his own hat must be black because B cannot see his own hat. Thus, C would insanity reason that his hat is black. Similar logic suggest that B would also reason his own hat is black as well. But the PAUSE would imply that neither immediately deduced this. Therefore, this is not the case: the case where your hat is red. Therefore, the only other possibility is your hat is black. But then again, if we assumed they all knew perfect logic as is the case with these types of problems, all three would conclude their own hat is black after the pause.

Scenario 1 Everyone wears red No-one raises their hands Explanation: "We are all wearing red because no-one raised their hands." Scenario 2 Two people wear red, one wears black. Two people raise their hands Explanation: "One of us is wearing red, the person wearing black didn't raise their hand" Scenario 3 Two people wear black, one wears red. Everyone raises their hands The people wearing black know they are wearing black because in Scenario 2 (2 red hats) two people not 3 would have raised their hands. However in this scenario all three have raised their hands and the black hat wearers can see one red hat. So there can only be one red hat. Scenario 4 - the trick scenario Everyone wears black The cleverest guy figures out "if I was wearing red then guys wearing black hats would realise they are wearing black hats because we all raised our hands (scenario 3) and they can see my red hat. But they didn't say they were wearing black and are still thinking about it - so we must all be wearing black hats. The puzzle relies on an extra step in logic, the first 3 scenarios are fairly easy to work out for someone in that situation. But the final scenario (4) requires you to visualise the other three scenarios to figure out the answer.