Mathematical Moving Chairs
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Number
of people ->
Multiply by ...
6
7
8
9
10
...
2
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3
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4
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5
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6
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Suppose we have 8 people in chairs
number
ed 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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