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Button-up

Stage: 1 Challenge Level: Challenge Level:1

My coat has three different buttons.
 
Sometimes, I do them up starting with the top button.  Sometimes, I start somewhere else.
 
How many ways can you find to do up my coat?
 
How will you remember them?
 
Do you think there are any more?  How do you know?

This problem was inspired by an idea of Bernard Murphy.