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

  • Thread starter Thread starter Werg22
  • Start date Start date
  • Tags Tags
    Cube Cut
Click For Summary
The discussion revolves around the challenge of determining the minimum number of cuts required to divide a cube into 27 smaller cubes. Participants agree that six cuts are necessary to achieve this, with the reasoning that each cut can effectively increase the number of pieces by dividing the cube into smaller sections. The conversation explores various cutting methods, including the use of a knife with dual blades, and the possibility of rearranging pieces before making subsequent cuts. Some participants suggest alternative cutting techniques, such as using acid, but these are dismissed as impractical. The consensus is that while creative methods may yield different shapes or sizes, achieving exactly 27 uniform cubes requires a minimum of six cuts. The discussion also touches on the theoretical maximum number of pieces obtainable with a given number of cuts and the implications of allowing rearrangement of pieces. Ultimately, the conclusion remains that six cuts are necessary to achieve the desired outcome.
  • #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:
 
Physics 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

So, can we see a cube instead of sphere?
  • · Replies 18 ·
Replies
18
Views
1K
I Higher Dimensional Spheres viz. Cubes
  • · Replies 1 ·
Replies
1
Views
1K
B Cube Math: How Many Smaller Cubes in a Larger Cube?
  • · Replies 4 ·
Replies
4
Views
4K
Where Can I Find a 1 mm Cube for Visual Demonstrations?
  • · Replies 17 ·
Replies
17
Views
3K
What Motor Setup is Needed to Rotate a 75 lb Cube at 6 RPM?
  • · Replies 2 ·
Replies
2
Views
1K
Electric field and potential at vertex of cube
  • · Replies 9 ·
Replies
9
Views
3K
Calculate the "surface energy" of succesively smaller cubes
  • · Replies 3 ·
Replies
3
Views
3K
No integer whose digits add up to ## 15 ## can be a square or a cube
  • · Replies 4 ·
Replies
4
Views
3K
MHB Can Two Points in a Cube Be Less Than √(3)/2 Apart?
  • · Replies 2 ·
Replies
2
Views
1K
MHB Can I Use the Difference of Cubes Formula for Factoring 27 - (a - b)^3?
  • · Replies 5 ·
Replies
5
Views
2K