September 9th, 2006

Froude number

math

I am a super-mega-dork, because I stayed up until stupid o'clock last night working on a math problem.

Technology Review (which all MIT alumni get) has a puzzle column, and I was reading it last night and got sucked in to the raquetball problem, which goes like this:

In racquetball, if the server doesn't score a point, the other guy gets to serve. Whoever gets 15 points first wins. If the score is 13 to 14, the guy with 13 points is serving, and we assume that whoever serves has probability p of scoring a point, what does p have to be for it to be more likely that the guy with 13 points will win the game?

The answer is, "a little bit more than 55% or greater", and you totally don't care where that comes from, but I feel like explaining it anyway. Luckily for you, I'm nice and will hide it behind a cut rather than inflict it upon you involuntarily. Collapse )

I also found a covering of the chessboard with 12 knights, but I can't prove that's the minimum number you need, though I'm pretty sure it is.

EDIT: I found a site that has knight coverings! Optimality proofs down at the bottom.