Pentagon Ring

Weekly Problem 47 - 2011
Place equal, regular pentagons together to form a ring. How many pentagons will be needed?
Age
11 to 14
Challenge level
filled star filled star filled star
Exploring and noticing Working systematically Conjecturing and generalising Visualising and representing Reasoning, convincing and proving
Being curious Being resourceful Being resilient Being collaborative

Problem



Equal regular pentagons are placed together to form a ring.  

The diagram shows the first three pentagons.

How many pentagons are needed to complete the ring?

Pentagon Ring

 

If you liked this problem, here is an NRICH task which challenges you to use similar mathematical ideas.