Find the least number of cuts required which can cut a cube into 24 identical pieces?
Answers
HI FRIEND HOPE THIS ANSWER HELPS YOU
The easiest case is slicing down through the top to get 6x4 vertical cuboids. This gives you 24 identical elongated cuboids with (6–1) + (4–1) or 8 cuts.
Systematically, how many ways can you factor 24 into 1, 2, or 3 factors? (3 for 3 dimensions)
24 x 1: slice the top in one direction 24 times. 23 cuts
12 x 2. Slice the top into 12 slices and the cut the middle once horizontally. 11 + 1 = 12 cuts
6 x 4: slice the top in 2 directions into 6 and 4 slices. 5+3 = 8 cuts
8x3: slice the top 8x3. 9 cuts
6x2x2: top into 6x2, then middle. 5+1+1 = 7 cuts
2x3x4: 2x3 on top, one in the middle. 1+2+3=6 cuts.
That’s all there is, so the winner is 6 cuts.
The solution: You can do it in a minimum of 6 cuts. Each face of the center cube must be cut once, and you can't possibly cut 2 faces of the same cube at the same time. Therefore, you need all 6 cuts to separate the 24 cubes.