Righteous hack: getting 263 - 1 points in a silly Facebook game

Security through obscurity doesn't work. Every once in a while I like to prove this fact, by getting worldwide high scores on vulnerable leaderboards. The first time I did this was to Area Flat 3 (which was an awesome game when I was in elementary school, and is still pretty fun). Check the all-time top 100 scores for H4X0R (I know, not very original; I was 13, sue me). But that hack was child's play compared to this one. Continue reading Righteous hack: getting 263 - 1 points in a silly Facebook game

Solving Polynomials

A well known (if not by name) theorem is the Abel–Ruffini theorem, which states that there is no algebraic expression for the roots of polynomials with degree higher than 4.

A not-so-well-known fact is that for any polynomial \(P(x)\), it is possible to find (with exact arithmetic) a set of ranges each containing exactly one root of \(P(x)\). One such algorithm is due to James Victor Uspensky in 1948. Continue reading Solving Polynomials