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        riddles >> hard >> Cutting a cube
        
(Message started by: BenVitale on Jan 31^st, 2008, 9:03pm)

Title: Cutting a cube
Post by BenVitale on Jan 31^st, 2008, 9:03pm

If you cut a cube of material with 5 perfectly straight slices all the way through?
What is the maximum amount of separate pieces you can create?

These links may help:

http://www.eskimo.com/~miyaguch/power.html

http://www.research.att.com/~njas/sequences/A000125

Title: Re: Cutting a cube
Post by towr on Feb 1^st, 2008, 12:27am

Can you move the pieces between cuts?
Do you have to cut parallel to the sides of the cubes?

Title: Re: Cutting a cube
Post by BenVitale on Feb 1^st, 2008, 2:57am

This is what i did :

The maximal number of pieces into which "n" planes divide the space, is given by:
(n^3 + 5n + 6)/6, so the answer to this question is 26.

What do u think? Do u agree with the solution?

Title: Re: Cutting a cube
Post by ThudanBlunder on Feb 1^st, 2008, 3:06am

on 02/01/08 at 02:57:45, BenVitale wrote:

This is what i did :
The maximal number of pieces into which "n" planes divide the space, is given by:
(n^3 + 5n + 6)/6, so the answer to this question is 26.
What do u think? Do u agree with the solution?

(n^3 + 5n + 6)/6 is a deus ex machina formula, not a solution. :P

Title: Re: Cutting a cube
Post by towr on Feb 1^st, 2008, 6:41am

I can get 32 if (and only if) I can move the pieces around for each planar cut.
If you have to make cuts parallel to the sides of the cubes (without moving pieces around), I get 18.
And 26 is a perfectly correct answer in the case you just divide the cube with random planes (without moving the pieces).