In Part I of this article, we described how to calculate the number of combinations of a combination lock, as well as the number of ways to arrange objects, instead of listing out each combination individually. In Part II, we…

Chapter 1: What is Combinatorics? Have you ever used a combination lock before? Two of the most common combination lock designs are shown below. Left: Combination Lock A, Right: Combination Lock B For Combination Lock A, there are 8 buttons…

We learn the two mechanisms of nucleophilic substitution in school, namely SN1 and SN2. To recap, SN1 is a two-step mechanism involving first the leaving of the leaving group to form a carbocation intermediate, which is then attacked by the…

Autonomous materials are materials that can protect itself, heal damage and indicate if it is damaged throughout the course of its life cycle without any active intervention. These materials are at the forefront of materials science research, as they hold…