How does Modular Arithmetic work?

Question 6 from Tom Rocks Maths and I Love Mathematics - answering the questions sent in and voted for by YOU. This time we explore modular arithmetic through the familiar example of the 12-hour clock.

Full playlist: https://www.youtube.com/watch?v=by8Mf6Lm5I8&list=PLMCRxGutHqfmb00xXx9n0VSZK85g82NI_

Q1: What is the probability I have the same PIN as someone else?
Q2: How long would it take to sink to the bottom of the ocean?
Q3: What is the gravitational field of a hollow Earth?
Q4: What is the best way to win at the board game Monopoly?
Q5: What are the most basic Mathematical Axioms?
Q6: How does Modular Arithmetic work?
Q7: What is the Gamma Function?
Q8: How many ping-pong balls would it take to lift the Titanic from the ocean floor?
Q9: What is the graph of x^x?
Q10: How can you show geometrically that Pi is between 3 and 4?

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