Which is the least possible number of cuts required to cut a cube into 64 identical pieces?

To cut a cube into 64 identical pieces, we need to consider the number of pieces along each dimension (length, width, height). Since 64 is 4x4x4, this means we need 4 smaller cubes along each of the three dimensions.

To get N pieces along one dimension, you need N-1 cuts.

1. Along the length: To get 4 pieces, you need 4-1 = 3 cuts.
2. Along the width: To get 4 pieces, you need 4-1 = 3 cuts.
3. Along the height: To get 4 pieces, you need 4-1 = 3 cuts.

The total number of cuts required is the sum of cuts along each independent dimension: 3 + 3 + 3 = 9 cuts.

Analyzing the options: A) 8: This would not yield 64 pieces (e.g., 3+3+2 cuts result in 4x4x3 = 48 pieces). B) 9: This is the correct minimum number of cuts (3 cuts in each of the three dimensions). C) 12: This is more than the minimum required (e.g., 4+4+4 cuts result in 5x5x5 = 125 pieces). D) 16: This is also more than the minimum required.

The final answer is B.