The Chinese remainder theorem is not a difficult concept but is one that comes up over and over again. We see it in primary school maths competitions, high school maths olympiads, university maths and even puzzle hunts.

Instead of resolving it each time you see it, we discuss here that one can identify it instead and reuse old insights. Problems involving this have been encountered as early as grade 5 where you might want to know when two clock hands meet at the same point on the clock or when racers meet each other during their laps, or sharing bananas between monkeys. This recurs in every level of competition all the way from the qualifiers to the USAMO. I even remember solving puzzle hunt problems based on this idea.

Here we present the theorem in different ways to show how one can learn the same thing in maths in more advanced ways and notice different aspects of it. We then work on some basic exercises to solidify the theorem in your mind. Some further problems are suggested.

In the theory, it comes under diophantine equations or simultaneous linear equations in mods. Harder topics mind include Pell's equation or Harder modular arithmetic.