Can a cube be cut in 27 smaller cubes in less than 6 cuts?

  • Context: Undergrad 
  • Thread starter Thread starter Werg22
  • Start date Start date
  • Tags Tags
    Cube Cut
Click For Summary

Discussion Overview

The discussion revolves around the question of whether a cube can be cut into 27 smaller cubes using fewer than 6 cuts. Participants explore various cutting strategies, definitions of a "cut," and the implications of rearranging pieces after cuts.

Discussion Character

  • Debate/contested
  • Exploratory
  • Mathematical reasoning

Main Points Raised

  • Some participants assert that 6 cuts are necessary to create a central cube, suggesting that this is the minimal number of cuts required.
  • Others propose that using a knife with two blades could reduce the number of cuts needed, although this is contested.
  • One participant describes a method to achieve 64 smaller cubes with 6 cuts, implying that achieving 27 cubes in fewer cuts might be feasible.
  • Another participant argues that if all smaller cubes must be the same size, then 6 cuts are required to ensure that each face of the central cube is cut.
  • Some participants discuss the possibility of rearranging pieces before making subsequent cuts, questioning how this affects the total number of cuts needed.
  • There are suggestions that different interpretations of "cut" could lead to varying conclusions about the number of cuts required.
  • A few participants mention the potential for creating more pieces than cubes, raising questions about the definitions of cubes versus parallelepipeds.

Areas of Agreement / Disagreement

Participants generally disagree on whether it is possible to achieve the goal in fewer than 6 cuts. While some maintain that 6 is the minimum, others suggest alternative methods that could potentially reduce this number, leading to an unresolved discussion.

Contextual Notes

Definitions of a "cut" and whether rearrangement of pieces is allowed remain ambiguous, impacting the conclusions drawn by participants. The discussion also touches on the mathematical implications of cutting strategies without reaching a consensus.

Who May Find This Useful

This discussion may be of interest to those exploring combinatorial geometry, mathematical puzzles, or the properties of three-dimensional objects in cutting problems.

  • #31
davee123 said:
Here's a question: what's the MOST number of cubes you can create with 6 cuts, allowing piece re-arrangement?
DaveE

This is much more easier : 64

:smile:
 
Mathematics news on Phys.org
  • #32
Rogerio said:
This is much more easier : 64

:smile:

Oh yeah-- duh, 3 cuts with re-arrangement obviously allows for 1 cube to be cut into 8, hence 8^2. Now just still need the less-than-6 cuts proven...

DaveE
 
  • #33
Use a device that makes multiple slices with each cut...not sure if this qualifies.
 
  • #34
Last edited by a moderator:

Similar threads

Undergrad Higher Dimensional Spheres viz. Cubes
  • · Replies 1 ·
Replies
1
Views
1K
High School Cube Math: How Many Smaller Cubes in a Larger Cube?
  • · Replies 4 ·
Replies
4
Views
4K
MHB Can Two Points in a Cube Be Less Than √(3)/2 Apart?
  • · Replies 2 ·
Replies
2
Views
2K
Undergrad Doubling a Cube: Can 3D Geometry Help?
  • · Replies 4 ·
Replies
4
Views
2K
MHB [ASK] Find the volume of Pyramid in a Cube
  • · Replies 6 ·
Replies
6
Views
3K
MHB How to Find the Cube Root of a Number?
  • · Replies 1 ·
Replies
1
Views
2K
MHB Prove (a²+b²+6)/(ab) is a perfect cube
  • · Replies 2 ·
Replies
2
Views
2K
Undergrad Dyadic cubes generate Borel sigma algebra of subset
  • · Replies 2 ·
Replies
2
Views
2K
Insights Fermat's Last Theorem
  • · Replies 105 ·
4
Replies
105
Views
9K
Undergrad Can a Cube Be Cut into Smaller Cubes of the Same Size?
  • · Replies 5 ·
Replies
5
Views
3K