2023 AMC 8 第 18 题
先试着解答 2023 AMC 8 第 18 题，然后核对你的答案与视频与精心整理的解答，解答来自 LIVE by Po-Shen Loh。你也可以参加完整限时模拟考试、查看全部 2023 AMC 8 解答，或核对答案。
所有题目均经美国数学协会（MAA）官方合法授权使用。
18.
蚱蜢格蕾塔坐在池塘中一长排睡莲叶上。从任意一片睡莲叶出发，格蕾塔可以向右跳 片，或向左跳 片。格蕾塔至少要跳多少次，才能到达从起点向右 片的睡莲叶？
Greta Grasshopper sits on a long line of lily pads in a pond. From any lily pad, Greta can jump pads to the right or pads to the left. What is the fewest number of jumps Greta must make to reach the lily pad located pads to the right of her starting position?
小提示：
先用 次向右跳到
Start with jumps to the right, which reaches
大提示：
额外跳跃的净位移必须为
The extra jumps must have net displacement
视频讲解：
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文字解答：
设向右跳 次，向左跳 次，则需要 模 化简得 ，所以 。
为了最少跳跃，取满足条件的最小 ，也就是 。此时 ，所以 。
总跳数为 。
所以正确答案是 D。
Let be the number of right jumps and be the number of left jumps. We need Reducing modulo gives , so .
To minimize the total number of jumps, use the smallest possible , namely . Then , so .
The fewest number of jumps is .
Thus, D is the correct answer.
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