I met a friend majored in math on a bus home today. He held a piece of paper with a question (probably an interview question since he is trying to find a job recently). He asked the question to me and I found it to be an interesting one.

A …

Suppose a poker games requires 4 decks of poker. After the game, the cards are put back into the 4 decks randomly. Now there is another game which requires only 1 deck of poker, so we want to open some decks of the poker and find a complete set of …

There are \(N\) seats on a plane. Suppose the first passengers is drunk and he takes a seat randomly. For each of the other passengers, if his/her seat is not taken by other people, then he/she sits on his/her own seat, otherwise he/she takes a seat …

Dating back to the time when I was a sophomore, I read a very interesting problem from "Waming", which is a magazine of math department of USTC (University of Science and Technology of China).

One day Guigu Zi (a famous ancient Chinese sophist, the teacher of Sun Bin and Pang …

Suppose a basketball player make \(N\) shots, and we know that in the first \(n(\le N)\) shots he sinked \(m(\le n)\) shots. If from the \((n+1)^{th}\) shot, his ratio of sink a shot is his accumulative ratio before the shot, e.g., suppose he sinked 40 …

I have to deal with Modified Bessel functions of the first kind frequently in my research. Here I list some useful properties of them for future reference.