What is the least possible number of cuts required to cut a cube into 64 identical pieces?
What is the least possible number of cuts required to cut a cube into 64 identical pieces?
8
9
12
16
Solution
Let $n$ be the number of small cubes along each edge. Then $n^3 = 64$, so $n = 4$. To get 4 pieces along an edge we need 3 cuts along that edge. Cutting along each of the three axes ($x$, $y$, $z$) gives $3 + 3 + 3 = 9$ cuts.