Mathematical Moving Chairs

   
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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!

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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