What is the least possible number of cuts required to cut a cube into 64 identical pieces?
- (a) 8
- (b) 9 ✓ UPSC's answer
- (c) 12
- (d) 16
Why the answer is (b)
• 64 = 4 x 4 x 4, so the cube is divided into 4 equal parts along length, 4 along breadth, and 4 along height.
• Dividing one edge into 4 equal parts requires 3 straight cuts.
• The same 3 cuts are needed in each of the three mutually perpendicular directions.
• Total cuts = 3 + 3 + 3 = 9, so option (b) follows.
Why the other options are wrong
- (a) 8
- 8 cuts cannot provide 3 cuts in each of the three dimensions needed for a 4 x 4 x 4 division.
- (c) 12
- 12 cuts are more than the 9 cuts needed for 3 cuts in each of the three dimensions.
- (d) 16
- 16 cuts are more than the 9 cuts needed for 3 cuts in each of the three dimensions.
Asked in the CSAT Paper II of the UPSC Civil Services Preliminary Examination 2024, held on 16 June 2024. Question and answer key: Union Public Service Commission. Explanation: UPSC Answer Check.