A cube is to be cut into 8 pieces of equal size and shape. Here, each cut should be straight and it should not stop till it reaches the other end of the cube. The minimum number of such cuts required is
A. 3
B. 4
C. 7
D. 8
GATE 2024 · General Aptitude · Patterns In Three Dimensions · medium
Answer: A. 3
Recognize the target: 8 equal mini-cubes: The only way to divide a cube into 8 congruent pieces with the same shape is to halve it along each of the three coordinate axes. This gives 2 layers in x, 2 in y, and 2 in z, producing 8 equal smaller cubes.
Count cuts needed: Cut 1: a horizontal plane midway through the cube (splits into top half and bottom half, 2 pieces). Cut 2: a vertical plane front-to-back through the midpoint (each half splits into two quarters, now 4 pieces). Cut 3: a vertical plane left-to-right through the midpoint (each quarter splits in two, now 8 pieces). All cuts go through the entire current arrangement in one pass.
Verify 2 cuts are insufficient: With only 2 through-cuts we can produce at most 4 pieces (cutting along 2 axes). We need 8 pieces, so 2 cuts are not enough. Thus 3 is the minimum.