AMC 8 2018 Problem 25
AMC8 2018 年第 25 题
特殊数与不定方程★★★★☆
How many perfect cubes lie between and , inclusive?
在 和 之间（包括 和 ）的完全立方数有多少个？
- A.4
- B.9
- C.10
- D.57
- E.58
正确答案 · Correct Answer
E
解析 · Solution
解法1
常规解法 · 定上下界
，，故最小合格立方是 。，，故最大是 。个数 =64-7+1=58。
巧解 · 识破
关键一眼：，所以上端正好卡到 ；下端 略过 落在 起。于是立方数恰为 ，共 58 个。
Solution 1
Elementary · find the bounds
Since and , the smallest qualifying cube is . Since and , the largest is . The count is 64-7+1=58.
Slick · spot that
The key is , so the upper end lands exactly on ; the lower end just passes and starts at . The cubes are exactly , which is 58 of them.
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