Copyright © University of Cambridge. All rights reserved.

## 'Counting Counters' printed from http://nrich.maths.org/

Jade from Coombe Girls School and Rohaan from
North Cross Intermediate correctly spotted the pattern in the
number of counters in each ring:

Every ring you add, you are just adding $6$ more counters than the
previous ring.

Circle number

excluding the counter in the
middle $\times6 = $number of counters

in that particular layer
Volkan and other pupils at FMV Ozel Erenkoy
Isik Primary solved the second part of the problem:

At the end of the third layer, there are; $1+6+12=19$
counters.

At the end of the fourth layer, there are; $19+(3\times6)=37$
counters.

At the end of the seventh layer, there are; $37+(15\times6)=127$
counters.

At the end of the ninth layer, there are; $127+(15\times6)=217$
counters.

Some people solved this part by numbering the
counters, starting from one in the middle and counting outwards.
Thank you for sending in your solutions!