wu :: forums
« wu :: forums - Cutting a cube »

Welcome, Guest. Please Login or Register.
Dec 22nd, 2024, 3:13am

RIDDLES SITE WRITE MATH! Home Home Help Help Search Search Members Members Login Login Register Register
   wu :: forums
   riddles
   hard
(Moderators: ThudnBlunder, SMQ, towr, Icarus, Eigenray, Grimbal, william wu)
   Cutting a cube
« Previous topic | Next topic »
Pages: 1  Reply Reply Notify of replies Notify of replies Send Topic Send Topic Print Print
   Author  Topic: Cutting a cube  (Read 3627 times)
Benny
Uberpuzzler
*****





   


Gender: male
Posts: 1024
Cutting a cube  
« on: Jan 31st, 2008, 9:03pm »
Quote Quote Modify Modify

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
 
 
IP Logged

If we want to understand our world — or how to change it — we must first understand the rational choices that shape it.
towr
wu::riddles Moderator
Uberpuzzler
*****



Some people are average, some are just mean.

   


Gender: male
Posts: 13730
Re: Cutting a cube  
« Reply #1 on: Feb 1st, 2008, 12:27am »
Quote Quote Modify Modify

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

Wikipedia, Google, Mathworld, Integer sequence DB
Benny
Uberpuzzler
*****





   


Gender: male
Posts: 1024
Re: Cutting a cube  
« Reply #2 on: Feb 1st, 2008, 2:57am »
Quote Quote Modify Modify

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?
IP Logged

If we want to understand our world — or how to change it — we must first understand the rational choices that shape it.
ThudnBlunder
wu::riddles Moderator
Uberpuzzler
*****




The dewdrop slides into the shining Sea

   


Gender: male
Posts: 4489
Re: Cutting a cube  
« Reply #3 on: Feb 1st, 2008, 3:06am »
Quote Quote Modify Modify

on Feb 1st, 2008, 2:57am, 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.   Tongue
IP Logged

THE MEEK SHALL INHERIT THE EARTH.....................................................................er, if that's all right with the rest of you.
towr
wu::riddles Moderator
Uberpuzzler
*****



Some people are average, some are just mean.

   


Gender: male
Posts: 13730
Re: Cutting a cube  
« Reply #4 on: Feb 1st, 2008, 6:41am »
Quote Quote Modify Modify

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).
IP Logged

Wikipedia, Google, Mathworld, Integer sequence DB
Pages: 1  Reply Reply Notify of replies Notify of replies Send Topic Send Topic Print Print

« Previous topic | Next topic »

Powered by YaBB 1 Gold - SP 1.4!
Forum software copyright © 2000-2004 Yet another Bulletin Board