# Mathematical Moving Chairs

One of the topics on which Colin Wright has given a Mathematics Talk.

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.

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