I proposed this problem in a birthday team competition I wrote, but at the time I asked for its equivalent in 18 dimension. Today I’ll explain it in 3 dimensions, and I want to point out that 3 is the perfect number for today’s occurrence. Now, how many parts of space (finite or infinite) can […]

# Category: Combinatorics

## Using Symmetry

I put this problem in an old team competition I organized. It is not simple, and I asked only for the case where n is even, now I’ll show you the complete version. Let be reals in an interval of lenght 1. Find the maximum value of Now, let’s treat as constants and let be […]

## Double Counting: Part 1

Double counting is a widely used technique of combinatorics, which consists of counting the same quantity with two different methods so that you can create an equation. Today I’m going to show you some of its application. Double Counting In A Polyhedron Does a polyhedron exist with an odd number of faces each having an […]

## Great Classic: Hanoi Tower

Tower of Hanoi consists of three pegs or towers with n disks placed one over the other. The objective of the puzzle is to move the stack to another peg following these simple rules. Only one disk can be moved at a time. No disk can be placed on top of the smaller disk. In […]

## Two Examples For The Box Principle

The box principle is a pretty simple yet so useful mathematical principle which asserts: If there are n+1 objects to put into n boxes, then 2 objects must be in the same box. This makes us think that usually we just have to divide our set of possibilities in mutually exclusive boxes and prove that […]

## An Insight Into Generating Functions

The technique of using a generating function is widely used in combinatorics: you have a polynomial where the coefficient of the term of degree n represents how many times n appears in your counting problem. Let’s see a simple example to make it clearer. Let’s say we have 2 standard dice, we roll both and […]