Mindbender: The Candidates

There was a good job going in the office and the boss could not decide which of the three candidates should have it, each of them being worthy of it and all of them very bright indeed. So he set them a problem and the one who solved it would get the job. He showed them five discs, three black and two white and said: ā€˜Iā€™m going to put a disc on the forehead of each of you. You will be able to see the others discs but not your own. There will be no talking. By pure deduction, you will have to work out what colour disc you have, and the one who does so gets the job.ā€™ He withheld the two white discs and put a black one on each of them. After a time one of the men stepped forward and successfully claimed the job. How did he figure out that he had a black disc on?



Call the candidates A, B and C... A gets the job through the following reasoning:-
If I had a white disc, then B would have gone into the office already, because he would have figured to himself,

"Well, I(B) can see A has white, which means if I(B) had white also, by now C would have figured that he can see two whites, that automatically makes me a black, so I must have the black marker because C isn't doing that."

And with B not doing that it told A he had a black marker.

Sent in by Jamie Salisbury

#9 could also be: The first man saw that, the boss had no preferance, than he would know that putting a white disk on his head and black disks on the other mens heads would be unfair and would mean that all men were not solving the same puzzle. (So two men were seeing two other men: one wearing black and the other wearing white while one man saw two men- both wearing black) By forcing one man to solve one puzzle and two other men solving a copletely different puzzle, the boss would have been unfair, and he knew that the boss would not and could not do that because he had no preferance. So because he knew that the boss would not be unfair and put a different color on one mans head than the others he could know that they all had the same color, and seeing that the other two men were wearing black, knew that he too was wearing black. (He could even solve this puzzle without observing the two other mens disks because he knew that they were all wearing the same color which meant that they were all wearing black because there were only two white and three men.)

Sent in by Robert Ehrlich

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