Mathematical Moving Chairs

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Suppose we have 8 people in chairs numbered 0 to 7. Each person multiplies their seat number by 5, divides by 8 (being the number of people) and keeps the remainder. That's their new seat.

Do they all go to different seats?

What about with 9 people?
What about 10 people?
What about 11 people?
What if we multiply by 4?
... or by 6?
... or by 7?

When does it work?

And why?

This is intimately related to Modulo Arithmetic.

One of the enrichment tasks on this web site.

CategoryMaths

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