Maximum number of identical pieces a cube can be cut into by making 16 cuts?
Answers
Given : a cube cut by 16 cuts
To Find : maximum number of pieces into which a cube can be cut by 16 cuts
Solution:
A cube cut by x , y and z cuts
Then number of pieces = (x + 1)(y + 1)(z + 1)
Maximum pieces are achieved when
x = y = z
16 is not multiple of 3 but 15 is
Hence 5 , 5 and 6 cuts will given maximum number of pieces
Maximum number of pieces
= (5 + 1)(5 + 1)( 6 + 1)
= 6 * 6 * 7
= 252
the maximum number of pieces into which a cube can be cut by 16 cuts is 252
Additional Info :
If rearrangement of pieces is allowed after each cut
then maximum number of pieces = 2¹⁶ as after each cut pieces can be doubled .
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