So I cheated, and the guy I cheated from came to the same number 22.
My way of getting there:
Lines:Pieces
1:2
2:(2+2)=4
3:(4+3)=7
4:(7+4)=11
5:(11+5)=16
6:(16+6)=22
Each new cut can add as many pieces as that line number.
I just saw the pattern +1,+2,+3,+4,+5,+6… to compute my answer. Made sense that cutting a 2-dimensional pie (circle) could add at most 1 more piece than the last iteration added.
Comments
Now, off to cheat.
My way of getting there:
Lines:Pieces
1:2
2:(2+2)=4
3:(4+3)=7
4:(7+4)=11
5:(11+5)=16
6:(16+6)=22
Each new cut can add as many pieces as that line number.