I saw this math quiz question today on the theydidthemath subreddit. Pi is obviously slightly bigger than 3.14, but I didn't know whether a higher power is more important than a higher base.
Turns out the answer is "sometimes" - depending on whether the number in question is larger or smaller than Euler's number. Explanation at the link is way over my head. Posted for those who enjoy such things.
I’ve come across the similar question e^pi versus pi^e. This requires knowledge of both constants to several digits, and you can do it without a calculator, but the surprising answer is that both are very close and you need to go to second order. But I’m so long out of practice with math, I can’t remember how I did it 30 years ago.
ReplyDeleteThe most amazing equation in math is that e to the power of (i times pi) plus one is zero. It ties together 5 of the most important mathematical constants into one equation.
The best I could do in such a situation would be to fart loudly and walk out.
ReplyDeleteI would just walk out of the interview. What nutcase interviewer asks stuff like this? Don't want to work there. Bye.
ReplyDeleteI am in general appalled that a lot of interviews seem to be tests more than interviews. Words have a meaning. If you want to test someone's advanced math skills, then call it a test. If you want to hire someone, you don't need nonsense like this.
There really are very view jobs where math skills like this are relevant. Presumably, no one who doesn't know this applies this would apply to such positions. Nor would any decent HR person invite people who don't. The only problem here being that HR people generally don't know math themselves.
First observation: in my experience, the goal of such a question is to see how the candidate approaches a difficult problem, hopefully a new problem so that they do not already know the answer. An answer to the problem is great, a correct answer is even better, but it is the analytical approach that is of interest, the "thinking process", if you will. If somebody just guesses, that is a bad sign (note: the proper follow-up question is to "explain your answer", so guessing becomes immediately clear).
ReplyDeleteSecond observation: in my experience, the interviewer is looking for multiple approaches. If the first attempt is inconclusive (or wrong), what does the candidate do next?
In the work environment, the interviewer wants to see how the candidate approaches and solves problems. A mature candidate will attack the problem and will seek help where appropriate. These kinds of questions can demonstrate this behavior. This means the candidate can ask questions of the interviewer such as initial conditions of the problem or boundaries for the solution.
Of course, your experience may vary, but that is how I taught my people how to interview. Underlying my observations is the assumption that the question is somehow related to a job skill for the position. The "why are utility covers round" questions are not productive - unless, of course, you are looking to hire a utility cover designer. In the case of a math problem, that could be appropriate for a technical position like teaching, engineering, programming, and similar. Probably not a useful question for an artist, writer, salesperson, or other position that lacks a need for a technical skill.
As to the question at hand, the mathematics, I have an answer but I am not confident enough to say it in public. I will poke at it to see if I can raise my confidence. Note: in an interview situation, blunder ahead rather than give up.