Mathematical Moving Chairs 


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!
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 BernersLee 