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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Quotation from
Tim Berners-Lee

Number of people -> Multiply by ...	6	7	8	9	10	...
2	. ? .	. ? .	. ? .	. ? .	. ? .
3	. ? .	. ? .	. ? .	. ? .	. ? .
4	. ? .	. ? .	. ? .	. ? .	. ? .
5	. ? .	. ? .	Yes	. ? .	. ? .
6	. ? .	. ? .	. ? .	. ? .	. ? .
...

Mathematical Moving Chairs

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