Chinese Remainder Theorem

The Chinese remainder theorem is not a difficult concept but is one that comes up over and over again. 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.