Problem:
How many perfect cubes lie between and , inclusive?
Answer Choices:
A.
B.
C.
D.
E.
Solution:
Note that and that . Also note that , so the perfect cube that is closest to and less than + is . Thus the numbers are precisely the perfect cubes that lie between the two given numbers, and so there are of these perfect cubes.
Answer: .
The problems on this page are the property of the MAA's American Mathematics Competitions