21 Jun '03 19:071 edit

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 hopefuls (ðŸ˜‰) awaiting interview. Now, the hiring officer has objective criteria such that given two candidates, the superior Answer Prancer can always be certainly determined. Hte hiring officer follows a very efficient strategy. He picks some M<N, rejects the first M candidates in line, and then hires the first interviewee after that who is better than ALL of his predecessors. This can be shown to be the strategy that maximizes his chances of hiring the best Prancer, under certain circumstances. The questions are:

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?

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 hopefuls (ðŸ˜‰) awaiting interview. Now, the hiring officer has objective criteria such that given two candidates, the superior Answer Prancer can always be certainly determined. Hte hiring officer follows a very efficient strategy. He picks some M<N, rejects the first M candidates in line, and then hires the first interviewee after that who is better than ALL of his predecessors. This can be shown to be the strategy that maximizes his chances of hiring the best Prancer, under certain circumstances. The questions are:

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?