Button-Up

My coat has three buttons. How many ways can you find to do up all the buttons?
Exploring and noticing Working systematically Conjecturing and generalising Visualising and representing Reasoning, convincing and proving
Being curious Being resourceful Being resilient Being collaborative

Problem



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.