Button-Up Some More

How many ways can you find to do up all four buttons on my coat? How about if I had five buttons? Six ...?

Exploring and noticing Working systematically Conjecturing and generalising Visualising and representing Reasoning, convincing and proving
Being curious Being resourceful Being resilient Being collaborative


You might like to have a look at Button-up before trying this problem.

 

I have a jacket which has four buttons.

Sometimes, I do the buttons up starting with the top button. Sometimes, I start somewhere else.  

How many different ways of buttoning it up can you find?

 

Look back at the number of different ways you found for buttoning up three buttons and four buttons.

Can you predict the number of ways of buttoning up a coat with five buttons?

Six buttons ...?  

 

This problem was inspired by an idea from Bernard Murphy.