1.5*1.5*0.8=1.8

todo: ~90 introductory NT problems, ~60 USAMO problems, ~30 functional equations, ~20 scattered geometry problems, ? omgwtfinequalities, do not throw up, stop thinking about fast food at unhelpful times, or go though any more peripheral neuropathy, or some other thing that happens to 0.1% of us 0.1% of the time.

Why is 1! + 2! + 3! + ... + n! never a perfect power if n > 3?

In a plane, two points determine a line; three points determine a circle; five points determine a conic section (with lots of degenerate cases and non-Euclidean anomalies, but you know.) Is there an analogous and equally symmetric family of planar linearish curves what is determined by a set of four points? Six? Seven? Eight?

(edit do almost all sets of 4 points determine parabolas?)

Hah I'm procrastinating on my puzzle hunt again