Question

What is the maximum number of identical pieces a cube can be cut into by 13 cuts?

Answer 1

A cube can be cut into 150 number of identical pieces by 13 cuts.

Solution:

First cut will divide the cube in 2 parts. The second cut along perpendicular direction will double the number of parts to 4, now the 3rd cut will also be in perpendicular direction which will double the 4 parts to 8. So totally 8 cubes can be formed with 3 cuts. All the 3 direction should be perpendicular to each other.

Note that 1 cut = 2 parts of cube, 2 cut = 3 parts and so on.

x cuts made along one plane results in x + 1 pieces.

Logic behind this is, divide the given number of cuts in 3 equal parts and put that many cuts on each perpendicular direction.

For obtaining identical pieces, cuts must be made parallel to 3 planes of the cube.

Let we made x, y, z cuts along all three planes such that (x+1)(y+1)(z+1) = t is maximum & x + y + z = 13.

Different combinations can be possible but t will be maximum in (4, 4, 5) cuts.

So maximum pieces = (4 + 1) * (4 + 1) * (5 + 1) = 5 * 5 * 6 = 150

Hope it helps ✌✌❤

Answer 2

A cube can be cut into 150 identical pieces by 13 cuts

Explanation:

• Divide the cube into 2 parts. The second cut made perpendicularly will make it into 4 parts. Make another cut perpendicularly and the initial 4 parts will double. Therefore, with 3 cuts 8 cubes were formed.
• X number of cuts made = x + 1 pieces  
• The maximum combinations possible is 4,4, and 5 cuts. Therefore maximum pieces  = (4+1) × (4+1)× (5+1) = 150