2018 AMC 8 Problems/Problem 25
Contents
[hide]Problem
How many perfect cubes lie between and , inclusive?
Video Solutions
https://www.youtube.com/watch?v=pbnddMinUF8 -Happytwin
https://youtu.be/ZZloby9pPJQ ~DSA_Catachu
https://www.youtube.com/watch?v=2e7gyBYEDOA - MathEx
https://youtu.be/rQUwNC0gqdg?t=300
Solution 1
We compute . We're all familiar with what is, namely , which is too small. The smallest cube greater than it is . is too large to calculate, but we notice that , which therefore clearly will be the largest cube less than . So, the required number of cubes is
Solution 2 (Brute force) VERY NOT RECOMMENDED
First, . Then, . Now, we can see how many perfect cubes are between these two parameters. By guessing and checking, we find that it starts from and ends with . Now, by counting how many numbers are between these, we find the answer to be
~ xxsc
See Also
2018 AMC 8 (Problems • Answer Key • Resources) | ||
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