Prerequisite Knowledge of Factorial Where magic happens We start off by asking the question: how many ways are there to arrange ...

Introduction We're all familiar with the equation  $x^2+y^2=z^2 (1)$  describing the relationship between the sides of ...

An irrelevant Biblical reference to illustrate that multiplication is prevalent in Combinatorics Introduction                  ...

Partition: Distinguishability We're interested in the question: how many ways to give out candies to kids? The answers will ...

Your rich uncle wants you! For motivation, let's consider this practical question. Your uncle owns a necklace shop. He wants to...

Introduction Imagine you're a creepy stalker whose curious pastime is to observe your neighbors through your super-telescope. Y...

Goal We seek to prove the famous Wilson Theorem:         $(p-1)! \equiv (-1) \pmod{p}$ for odd prime $p$ The easy way to prove...

 Source: Pinterest Card shuffle and nerdy things  You get together with your friends to play Poker. Five minutes into the game and yo...

Prerequisite This article assumes basic knowledge of congruence (what it means ect...), if you find this assumption outrageo...

Suppose you have three friends Alice , Bob and Conor , who are wondering in how many different ways they can seat in a row of three c...