Combinatorics is a field of Mathematics that allows us to efficiently count numbers. It includes topics such as probabilities, permutations and combinations. It has applications in many areas outside Mathematics. In this article I will describe some problems related to Combinatorics.

Combinatorics is a field of Mathematics that allows us to efficiently count numbers. It includes topics such as probabilities, permutations and combinations. In this article I will describe how to solve a problem in Combinatorics that involves numbers between 0 and 9999.

In the N Diagonal problem, we have a board containing NxN squares. Each square can have 2 diagonals, but the diagonals of neighboring squares should not intersect. A square can have three possible states. Either empty, a left diagonal or a right diagonal. We need to find out if it is possible to have X number of diagonals.

Recursion is one method for proving statements mathematically. It is a powerful concept that has important applications in Computer Science. In this article I will describe how to use the technique of Recursion to prove a statement mathematically.