In room 1 we had a go at this problem. The idea was to use our algebra skills to come up with a rule that works for all rings, no matter how big. Here we are trying to figure out a pattern...

Counting Counters

Stage: 2

Take a counter and surround it by a ring of other counters that MUST touch two others. How many counters do you need to do this?

Imagine surrounding this ring with more counters.
How many more counters are needed now?
How many counters will there be altogether?

Were you right?

What about a bigger ring? And another? And another?

How many counters will there be in the

9th ring?
How many do you think there will be in the

100th ring?
How would you predict how many counters there will be in any ring?