A 'Black or White' Logic Puzzle ... For Intellectuals Only, Please?!


Question: A 'Black or White' Logic Puzzle !.!.!. For Intellectuals Only, Please!?
Three very intelligent individuals were applying for the position of an Analyst in one of the top scientific companies in the country!. The HR manager, after conducting a series of exams and interviews with them, could not decide which of the three would suit best for the position, so he brought them to a room without mirrors!. There he put one colored marker at the forehead of each applicant in such manner that the applicant could not see his own marker but could see the marker of the other two!. The marker could only be either white or black!.

The manager then announced, "If you see at least one Black marker on either person, raise your right hand!." All three of them raised their right hand!.

"The first person to correctly guess the color of the marker on his forehead, gets the position!."

After quite some time, the most intelligent of the three announced the color of his marker!. He got the job!.

What was the color of his marker and why !?

(no philosophical answers please)Www@Enter-QA@Com


Answers:
Let's name them 1,2,3!.
1 is the smart guy, and here is how he thinks:
1 is assumming that he has a white marker!.
Now 1 will walk in 2's shoes to think:
2 now is seeing 1 white and 1 black (say 1 is white and 3 is black)!.In that case, 2 is smart enough to know that he's not white!. Because if 2 is white and 1 is white, 3 will see 2 white markers, and he would not raise his hand!. So 2 will know that he's not white and gets the job!. But 2 is not doing anything!.
So 1 knows that 1 doesn't have a white marker as he presumed!.
He has the black one!.
and the fact is everyone has a black markerWww@Enter-QA@Com

something along the lines of!.!.!.
a is the intelligent one, with his mates b and c

they can all see at least one black marker and a can see b and c 's markers!.
if he can see b is black and c is white, then he knows his is black as b can see a black

if b and c are both white, then his must be black as they can see a blackWww@Enter-QA@Com

If everyone can see a black - there can't be two white markers!. I don't think they are all black either as then there wouldn't be enough information for anyone to work out their marker!.
Anyone that can see both a black and a white marker knows his must be black or all three would not have raised their hands!.Www@Enter-QA@Com

Black!.

The reason he knew he was marked black was because he saw that one of the others was white!.

Therefore he new that the other one who was marked black had put his right hand up because he saw that his mark was black!.Www@Enter-QA@Com

man # 1 saw at least 1 black mark as per instuction !. So the other mark was white, man # 2 also saw exactly the same !. man # 3 saw only black marks and that makes his white !. And he got the job !.Www@Enter-QA@Com

black!. there all black!.Www@Enter-QA@Com

BLACK! Since all raised their hands it is obvious that all the markers were black!!!!.Www@Enter-QA@Com

Black because all 3 markers were black!.Www@Enter-QA@Com

Black, all 3 of them saw a black marker on the other 2!.Www@Enter-QA@Com

The man who guessed the colour was a black man!.Www@Enter-QA@Com

blackWww@Enter-QA@Com

Excellent puzzle!!

One assumption here goes against your use of the word "guess"!. Given that the candidates are intelligent, I will assume that the winner did not "guess" the correct color!. The answer was given because the candidate KNEW it had to be correct!.

also, to avoid having to use he/she and him/her, I'm assuming that the winner is female, even though I'm proud to be male!. :)

The person that got the job, let's call her candidate #1, had a black marker!. Here's why:

When #1 looked at the other two foreheads, she could have seen three marker variations on #2 and #3 (order does not matter): B and B, B and W, or W and W!. Let's examine those three possibilities:

If #1 saw B and B, then #1 could not be sure what color was on her forehead since the Bs on the other two would allow everyone to see B!. Thus, B and B is eliminated!.

If #1 saw W and W, she could not have raised her hand!. Thus, W and W is eliminated!.

That leaves B and W as the only possible marker variation that #1 saw on the other two candidates!. Now let's examine the two options for her marker:

If #1's marker is W, then one of the other candidates could not have raised their hand!. With B and W on #2 and #3, and a W on #1, one of the other two candidates would have seen two white markers!. Since all raised their hands, W is eliminated as the marker on #1!.

That leaves B and W for candidates #2 and #3, and B for the winning candidate (#1) as the only possible solution!.Www@Enter-QA@Com



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