Imagine you are sitting in a circle with 12 friends, and from a designated starting point, every third person gets eliminated out of the circle. The last person sitting wins one million dollars. Could you figure out where to sit to outlast every other player and end up the winner? What if we extend it to a circle of 500 people or 1000 and what if every 5th, 26th, or 73rd person is eliminated? What I just described is known as the Josephus Problem.
The answer to this problem, along with many others, can be found in the mathematical concept of Modular Arithmetic. Modular arithmetic, often called clock arithmetic, acts like a clock with its circular nature, which you will soon discover. This website will lead you through some of the background, explanation, and applications of modular arithmetic. The goal of this website is to provide a clear exploration of this topic.
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