- #1
gjorgensen
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Homework Statement
I have been asked to find a recursive formula for the number of parts of a cuboid after n cuts, and then prove my formula.
The Attempt at a Solution
I have through a 3D drawing program figured out a the number of parts after 8 cuts
cuts, parts
1,2
2,4
3,8
4,15
5,25
6,38
7,54
8,73
I have noticed a relationship for n >2, which is that R(n+1)=2R(n) - (R(n-1)+3)
However I am looking for a recursive formula which will work for all n, and I have no idea how to prove this...
I would appreciate all the help I can get!
In advance, thank you!