Most recent change of MathematicalMovingChairs

Edit made on May 22, 2014 by ColinWright at 12:47:03

Deleted text in red / Inserted text in green

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[[[>
| Number of people -> ---- Multiply by ... | 6 | 7 | 8 | 9 | 10 | ... |
| 2 | . ? . | . ? . | . ? . | . ? . | . ? . |
| 3 | . ? . | . ? . | . ? . | . ? . | . ? . |
| 4 | . ? . | . ? . | . ? . | . ? . | . ? . |
| 5 | . ? . | . ? . | . ? . | . ? . | . ? . |
| 6 | . ? . | . ? . | . ? . | . ? . | . ? . |
| ... |
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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?
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This is intimately related to Modulo Arithmetic.

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One of the enrichment tasks on this web site.
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CategoryMaths