How do you run this selection process? One way to do this is to ask the applicants who are all the candidates who can do the job. But this is a lousy way. Some people might simply say they are qualified even though they are not.
Recruiters obviously need some way to filter out the candidates who cannot do the job. But let's say that even after doing that, the number of qualified candidates are still greater than N. What do you do now? Obviously, the company should hire those individuals who, when hired, maximizes the value to the firm over the tenure of the candidate at the company.
Obviously, the company cannot simply ask the candidates who are the most valuable, because each person might respond that it is they themselves.
So, the company is ultimately looking for certain signals. These signals, if present, indicate that the candidate, when hired, will bring maximum value to the company over their tenure.
However, once the candidates understand that these are the signals that a company is looking for, they can fake it[1]. For example, in this case, the candidate figured out that the company asks toy problems in the interview and memorized the answer, albeit in this case, accidentally. However, nothing is stopping a candidate from doing this deliberately. In this case, the author is reliably able to emit this "toy problem solving skill" signal even though he may not have been able to solve the problem in the time allotted during the interview. However, the company was unable to detect this possibly false signal and therefore, he was hired. In this case, it does not look like a bad outcome for most people involved
This problem of minimizing false positives would be an interesting problem to solve. A company that solves this problem well will probably enjoy a huge competitive advantage in the market.