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File: MathematicalMovingChairs One of the topics on which ColinWright has given a MathematicsTalk. Suppose we have 8 people in chairs numbered 0 to 7. Each person multiplies their seat number by 5, divides by 8 (that being the number of people) and keeps the remainder. That's their new seat. Do they all go to different seats? Yes they do! * What about with 9 people ... does it still work? * What about 10 people? * What about 11 people? * What if we multiply by 4? * ... or by 5? * ... or by 6? When does it work? | Number of people -> ---- Multiply by ... | 6 | 7 | 8 | 9 | 10 | ... | | 2 | . ? . | . ? . | . ? . | . ? . | . ? . | | 3 | . ? . | . ? . | . ? . | . ? . | . ? . | | 4 | . ? . | . ? . | . ? . | . ? . | . ? . | | 5 | . ? . | . ? . | #Yes# | . ? . | . ? . | | 6 | . ? . | . ? . | . ? . | . ? . | . ? . | | ... | And why? This has connections with cryptography, juggling, computer algorithms, telling the time, and loads of other mathematics.