What is the maximum number of identical pieces a cube can be cut into by 15 cuts.

To find the maximum number of identical pieces a cube can be cut into by 15 cuts, we can break down the problem step by step:

Step 1: Start with a cube. Step 2: Make the first cut to divide the cube into two identical halves. Step 3: Make the second cut perpendicular to the first cut, dividing each half into two equal parts. Now we have four identical pieces. Step 4: Make the third cut perpendicular to the first two cuts, dividing each of the four pieces into two equal parts. Now we have eight identical pieces. Step 5: Make the fourth cut perpendicular to the first three cuts, dividing each of the eight pieces into two equal parts. Now we have sixteen identical pieces, which exceeds the maximum number of pieces we can have with 15 cuts. Step 6: Therefore, the maximum number of identical pieces a cube can be cut into by 15 cuts is 16.

Please note that this answer assumes that the cuts are made in a way that each cut intersects all previous cuts and that the cuts are made in a consistent manner.