@XanderHenderson I learned to avoid to use "looks like HW". The construct causes confusion. I think it is best to avoid any reference to HW. It is not really key if it is HW. Theoretically looks like HW is a good way to put it, but it does not work well in practice.
@Surb tangentially, it is ultimately irrelevant whether it is homework. The presentation should have included more context, regardless to it being homework or not. "Looks like" should be understood in a literal sense, not as an insinuation that it is homework. Anyway, I'll stop here. Fortunately OP included some more information by now. — quid ♦1 min ago
What do y'all think of this question? From the comments, I have learned something new, and there is probably an interesting question buried in there somewhere, but I don't see that question being asked.
In the current incarnation, it looks pretty unmotivated and context-free.
I'd kind of like to see the question improved, but I'm not sure what advice to give.
Possibly the most striking proof of Archimedes's inequality $\pi < 22/7$ is an integral formula for the difference:
$$
\frac{22}{7} - \pi = \int_0^1 (x-x^2)^4 \frac{dx}{1+x^2},
$$
where the integrand is manifestly positive. This formula is "well-known" but its origin remains somewhat mysterious....
Although this specific question does not ask about calculating the integral, so it probably cannot be considered duplicate of the ones I found. The OP wrote: "Is this relationship purely an example of a mathematician searching for an equation that satisfies it, or is there a deeper, (possibly geometric), reason?"
In a school there are 1200 students. Each student must join exactly $k$ clubs. Given that there is a common club joined by every 23 students, but there is no common club joined by all 1200 students, find the smallest possible value of $k$.
I do not have any solution
This answer needs help. Personally, I would recommend that such help come in the form of deletion, but someone with a great deal of patience and free time could try to TeXify it.
@amWhy In an Australian sudoku site I frequent they have developed the greeting: Good maeN! As in Morning/Afternoon/Evening/Night. You are expected to put the part of the day current in your timezone in upper case (as I just did). It would not surprise me to hear that this was invented ages ago.
@quid My understanding has always been that "evening" is roughly the time between when twilight and bedtime; say (approximately) between 5-6 PM and 9-11 PM
or, if you prefer, roughly the time between getting home from work and bedtime
@Shaun You may want to avoid singling out individual users. There has been some recent controversy about the meaning of the "be nice" policy, and there is at least one active and vocal user who objects to linking to user profiles.
Ack... @amWhy is not @quid. You are both blue, therefore you must both be the same person.
(My students get pissy when I tell them that if their last name starts with the same letter as someone else's last name, then they must be the same person.)
In a school there are 1200 students. Each student must join exactly $k$ clubs. Given that there is a common club joined by every 23 students, but there is no common club joined by all 1200 students, find the smallest possible value of $k$.
I do not have any solution
