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Buffon's Needle

Draw lines y=n (n=...,-2,-1,0,1,2,...) in XY-plane. A needle of length one is thrown randomly onto the plane, what is the probability that it intersects some lines?

Make Palindrome

By definition palindrome is a string which is not changed when reversed. "MADAM" is a nice example of palindrome. It is an easy job to test whether a given string ...

Cube coloring problem

You have a normal six sided cube. How many different cubes can you make by painting each side using one of six colors?
If you can rotate two cubes to ...

Decomposing a convex n-gon into triangles

(1) In how many different ways can a convex n-gon be divided into triangles by nonintersecting diagonals?

(2) In decomposing a convex n-gon into triangles by drawing nonintersecting diagonals, ...

LRU cache

Design the data structures and algorithms for an LRU (Least Recently Used) Cache.