Petya and Vasya play a game, alternating turns in the usual way. Petya starts by choosing a polynomial P(x) with integer coefficients.. Each time that it is his turn, Vasya gives 1 dollar to Petya and tells him some integer a. Vasya cannot choose the same number twice. Except for his initial turn, Petya responds to Vasya by telling him the number of integer solutions to P(x)=a.Vasya wins when Petya tells him a number that was already reported by him (not necessarily on the preceding move). Determine the minimum number of dollars sufficient for Vasya to win the game for sure.
I'm really starting to get comfortable with Ableton Live and it's just so much better for composing unplayable music (and composing with sound) than Musescore. Musescore is more of a software for creating sheet music for others to perform, but no-one will ever perform any my compositions, so I'm going to make the most of this situation and learn to do everything myself.
I'll still be here because my mathematical thoughts are too stupid for proper math forums. :P
Confession time... I'm only in year 11 right now. Some of you are probably undergrads, but most you are above me. I doubt any of you are PhDs (or even PhD students) because in this age of overspecilaisation, what are the chances that one of those people are on Musescore?
...So, I really don't deserve to be the only admin. I'm trusting you to be mature enough to not do anything stupid, because you can still see the beauty of math despite having it butchered and forced down your throat since childhood.
Also, I'm insane (but still sane enough to manage daily life on my own).