Deleted text in red / Inserted text in green

WW

HEADERS_END

[[[>

| Number of people -> ---- Multiply by ... | 6 | 7 | 8 | 9 | 10 | ... |

| 2 | . ? . | . ? . | . ? . | . ? . | . ? . |

| 3 | . ? . | . ? . | . ? . | . ? . | . ? . |

| 4 | . ? . | . ? . | . ? . | . ? . | . ? . |

| 5 | . ? . | . ? . | . ? . | . ? . | . ? . |

| 6 | . ? . | . ? . | . ? . | . ? . | . ? . |

| ... |

]]]

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