Originally posted by royalchickenWhat does the hiring officer do if the best candidate is one of the first M? Surely this would mean that none of the remaining N-M candidates would be better than all their predecessors.
NOTE: THis is the first in a series of puzzles I've invented that feature RHP personalities. Enjoy.
Acolyte has decided to avoid the fate of the destitute student, and find gainful employment. His area of expertise being Answer Prancing, he heads down to Ans., Prance, & Dance to apply for a job. He joins the ranks of N purple-hose clad prancer h ...[text shortened]... cing skills, but does not know if he is the best. In what position in the line should he stand?
Originally posted by AcolyteAh. By "better than all predecessors", I mean "better than all previously intervied, i.e all that were not rejected out of hand." THere is a chance the best on wll be rejected, but say, for example, the 9th-best is the second-best among the remaining N_M, but the 8th-best occurs after he does. THen the 9th-best gets the job.
What does the hiring officer do if the best candidate is one of the first M? Surely this would mean that none of the remaining N-M candidates would be better than all their predecessors.
Also, is it fair to assume that 'better than' is transitive (ie if A is better than B and B is better than C, then A is better than C)?
Originally posted by royalchickenThe way I've understood this problem, the hiring officer is going to evaluate M-1 candidates, where the best fitted prancer of them always is chosen.
1. What value of M, in terms of N, should the officer use to maximize the probability of getting the best candidate?
2. If he picks the correct M, what is the probability he picks the best prospective Prancer?
3. Acolyte, who is a skilled mathematician, wants to maximize his chances of getting a job. He is confident of his prancing skills, but does not know if he is the best. In what position in the line should he stand?
Originally posted by royalchickenHumm. The probability could be as high as 1, but that wouldn't be very efficient. It would be very efficient, though, if one would interview just the last person in the queue. The probability would in that case be as low as P = 1/N
I perhaps expressed myself wrong or unclearly. He is going for the best probability of getting the Paramount Prancer while minimizing the number of interviews.
Originally posted by royalchickenDoes that mean that if the second person interviewed is better fitted than the first, he will be automaticly hired? (Even if the prancer best suited at is at the end of the queue?)
He picks some M less than N, rejects the first M candidates in line, and then hires the first interviewee after that who is better than ALL of his predecessors.
Originally posted by royalchickenSurely then he will always pick the first person he interviews, as they are trivially better than everyone interviewed before them.
Yes, basically. It goes like this: The first M are rejected. He then starts interviewing the remaining candidates as they are placedin line. As soon as he finds one, say, for example, the second best of all of them, who is better than all those interviewed before him, he hires him, even if, for example, the absolute best was the next man in line.
Hint: The best M is not a rational number.