Thank you for your quick reply. I did have a reasoning that led to the formula.

# cuts # pieces

0 1 start with 1 piece for 0 cuts
1 2
2 4
3 7

For every cut, the maximum lines you can intersect with is the previous number of cuts. So the maximum number of pieces bisected is (previous cuts 1), which is the current number of cuts. To get to the total number of pieces you have to subtract the pieces you didn't bisect, which is your previous total number of pieces minus current bisected pieces.

in formula that would be current cuts * 2 (prev total - current cuts) which is current cuts previous total

The 'previous total' is (x-1) (x-2) (x-3) .... 1 (add the one because of the original piece for 0 cuts)

This is how I got to x (x-1) (x-2) (x-3) ..... 1

I think this is correct, but since my math skills are quite rusty, and my niece's math teacher (who gave her the problem in the first place) appears to disagree with this, I thought I'd get the advice of an experienced mathematician.

Thanks a lot for your time, and I hope my explanation was not too
confusing.

Paul.