Question

Find the ratio between the maximum and the minimum number of pieces that can be obtained by cutting a cube 16 times.

a. 252 : 17
b. 21 : 5
c. 64 : 3
d. 14 : 1

Option (a)

• A. 252:17
• B. 21:5
• C. 64:3
• D. 14:1

Answer 1

The correct option is A 252:17

If the number of cuts is given, maximum pieces can be obtained when the cuts made in each plane are equal (a = b = c) or these three are as close as possible.
Minimum number of pieces can be obtained if all the cuts are made in one plane.

For maximum number of pieces, we will take a = b = 5 and c = 6
Number of pieces = (5+1)*(5+1)*(6+1) = 252

For minimum number of pieces = 16+1 = 17 pieces

Required ratio is 252 : 17