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Prove or disprove that a cube can be cut in 27 smaller cubes in less than 6 cuts

T

True Position

#11
What's a cut?

Is it when a tool enters a volume of material, and proceeds through the mass--ignoring intermediate seams at right angles to the cut line, where one piece of material is butted up against another piece--until it comes out the other side/end of the volume?

Or is it a certain length or area of cutting? Or does it have to be a certain shape of cut?
It's not much of a puzzle if you're allowed to cut whatever shapes you want.

(It's a math puzzle not a manufacturing problem)
 
H

Hodgepodge

#13
It cannot be done in less than 6 cuts. If the cube is to be cut into exactly 27 pieces, it would require 6 cuts. Even if it could be cut into more than 27 pieces, the quantity requires more than 5 cuts. The max # of cubes I could get in 5 cuts was 24.

When I read True Position’s post…
(It's a math puzzle not a manufacturing problem)
...I started thinking about it as a geometry problem. To cut a cube into exactly 27 equal pieces, a cube must be cut out of the center of the original cube. That “middle” cube requires all 6 sides to be cut, meaning a minimum of 6 cuts. It doesn't matter how many times or ways the pieces are stacked.
 

Qara123

Involved In Discussions
#14
The best I can get is to cut a cube 5 times and get 27 cubes/cuboids. That is, I get 1 large cube, 4 med cuboids, 6 small cuboids & 16 smaller cubes. Alternatively, cuts can be arranged to make 1 large cube, 10 med cubes & 16 small cuboids.

So while I can get 27 pieces in 5 cuts, I can't get them all to be cubes... shucks...

Q
 
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