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?