# Pentagon Ring

Weekly Problem 47 - 2011

Place equal, regular pentagons together to form a ring. How many pentagons will be needed?

Place equal, regular pentagons together to form a ring. How many pentagons will be needed?

## 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?

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

## Student Solutions

Each pentagon has a turn of 36^{o} to pack against its neighbour.

Therefore it will take 10 (x36^{o}) turns to complete a full-turn, i.e. 10 pentagons

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