If It Fits, Wear It.
Three candidates apply for a job, lets call them A, B and C. After the interviews the owner of the company doesn't know which one to choose as they are all of equal ability. He decides on a simple test of deduction. He says to all three that he has five hats, three which are red and two which are blue. He asks all three to close their eyes and explains that he is placing a hat on each of their heads. When he has finished he hides the two remaining hats. He then asks all three to open their eyes. He then says the first one to correctly deduce which colour hat he is wearing will get the job, explaining that each candidate can look at the other two but not remove their own hat.
The owner then says to candidate A which colour hat do you have on. The candidate says I do not know.
The owner then says to candidate B which colour hat do you have on. The candidate says I do not know.
The owner then says to candidate C which colour hat do you have on. The candidate says a red hat and he was correct and got the job.
How did candidate C know he was wearing a red hat?
There are no mirrors in the room.
11 Answers
When A did not know, B realized that A did not see two blue hats. When B did not know, C realized that neither A nor B saw two blue hats. If C's hat was blue, B would have know that his own hat could not also be blue (otherwise A would have known). Therefore, since neither A nor B were able to determine the color (colour) of their own hat, C knew his hat must be red.
This is the correct answer, but I cede to Abuelita who got it just seconds before I did. And to Micael who posted a correct answer while Abuelita was typing in her answer.
This is an unfair test conducted by the employer. Neither A nor B had a chance. To make it fair, the employer should have allowed the first to figure it out to speak up, not ask them in sequence. When any of the three realized that the other two did not know, he would have been able to deduce his own hat was red.
A and B should sue the employer for unfair hiring practices. Maybe the award would a lifetime supply of red and blue hats.
Cuando A no sabía, B se dio cuenta que A no había visto dos gorros azules. Cuando B no sabía, C se dio cuenta que ni A ni B vieron dos gorros azules, y sabía que B habría sabido que su propio gorro (de B) no era azul. Por tanto, siendo que ni A ni B pudieron adivinar el color de su propio gorro, C sabía que su gorro (de C) tenía que ser rojo.
Es una prueba injusta hecha por el patrón. Ni A ni B tenía oportunidad de ganar. Para hacerlo justo, el patrón debía haberlo permitido hablar el primero que adivinó el color de su gorro, y no preguntarlos en orden. Así, cuando cualquiera de los tres supiera que ninguno de los otros sabía, él habría podido deducir que su propio gorro fue rojo. Creo que esta es una instancia de prácticas injustas de empleo. A y B deben entablar demanda.
If A knew the answer then he would have said it right? And the only way he could have answered was if he had seen 2 blue hats on B and C. He didn't answer so obviously there was at least one red on B or C. So there might have been 2 reds or 1 red and 1 blue on B and C.
Then B would have known this when A didn't answer, so he would have known that either C or himself had at least one red. If B had known the answer then he would have right? He would only have been able to though if he had seen blue, because there needed to be at least one red and if he had seen blue on C then he(B) would have had to be wearing blue. But he didn't answer, so he must have seen red on C.
If B had seen red on C, then B could still be wearing either color. Again B didn't answer, so B MUST HAVE SEEN RED ON C. C knew this because B didn't answer, so C knew he was wearing red. If you were confused where I got that last sentence, check the caps.
If you need explanation, just comment. Just to make people feel bad, I'm 13!
Lets make this a little more difficult because you are not explaining the reasoning. The three are standing in a line facing a wall.
C is facing the wall and cannot see either A or B
B is behind C and can only see C
A is behind B and can see B and C
Explain the reasoning now that C knew he had a red hat on.
When A looked, if he had seen two blue hats, he would have know that he had on red; he said he didn't know so that tells us either B or C or both were wearing red.
From A's answer, B knows that either he, C or both of them are wearing red (because they cannot both be wearing blue). If he saw a blue hat on C, he would know that his must be red. Instead, he sees a red hat on C and still doesn't know what color his hat is.
C knows from A's answer that either he, B or both must be wearing red. If B had seen a blue hat he would have know his own hat color, but he did not know, therefore C knows that his own hat must be red.
A did not know therefore at least one of the two hats had to be red. (If he had seen two blue he would have known) B knew from A's lack of knowledge that there had to be at least 1 red hat. B didn't even have to look at A If B had seen blue on C he would have known that he was Red. Since he didn't know C knew immediately that he was red.
If it's a test of deduction and there are more red hats then blue hats then the choice would certainly be to say red simply because there is a higher chance of getting a red hat than a blue one although I presume there is some other, more difficult explanation.
A and B have on blue hats of which there are only two therefore C must be wearing a red hat. Very unfair for A and B.
I thought about how I could show the process of elimination to prove that Applicant C had a red hat. The following table shows all possible combinations, with lines 1, 2 and 3 including two blue hats, and lines 4, 5 and 6 including only one blue hat. Line 7 shows no blue hats.
- A B C
- Line 1 Red Blue Blue
- Line 2 Blue Red Blue
- Line 3 Blue Blue Red
- Line 4 Blue Red Red
- Line 5 Red Blue Red
- Line 6 Red Red Blue
- Line 7 Red Red Red
If line 1 is true, the Applicant A would know immediately that his hat was red. He did not know, therefore line 1 is eliminated. If line 2 is true, Applicant B would know immediately that his hat was red. He did not know, so line 2 is eliminated. If line 6 is true, Applicant B would know that since Applicant A saw at least one red hat (because A didn’t know the color of his own hat) his hat (B’s) must be red. B still doesn’t know the color of his hat, eliminating line 6. All remaining lines require that C have a red hat. Therefore, since neither A nor B were able to determine the color of their own hats, C must be wearing a red hat.
I hope the table still looks like a table when I post this.
Si A responde que sabe, es porque B y C están usando gorros azules.
Si B responde que sabe, es porque A y C están usando gorros azules.
C sabe que sólo puede estar usando color rojo, porque A y B respondieron que no sabían.
If A answers he knows, that means B and C wear blue hats.
If B answers he knows, that means A and C wear blue hats.
C knows he can only wear a red hat, because A and B answered they did not know.
If candidate C sees that A and B are wearing blue hats, he knows he has a red hat.
Is it for sure that C 'knew' he had on a red hat or did he get the job because he was the only one who spoke up/gave an answer?
I am going to bed now. I will post the answer tomorrow afternoon if no one gets it by then.
Congratulations to Calvo, AWC17 and Abuelita for an in depth explanation. I get the feeling that Carlos also knew but his explanation wasn't as precise.
