There's a problem which goes like this :
A monkey had some peaches.
He ate half of them plus one
On the second day, he ate half of
the rest plus one more.
On the third day, he ate half of
the rest plus one more again.
On the fourth day, he found there
was only one left.
How many did he have at the
By the time you reach Stage 4 you will start to feel that problems
like this are examples or instances of something more general.
Try this problem as it is and then generalise your solution as far
as you think you can.
Using a spreadsheet may be a help, but you can judge that for