2026 AMC 8 第 22 题
先试着解答 2026 AMC 8 第 22 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 2026 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。
22.
将整数 到 任意分成五组，每组 个数。找出每组的中位数，再在这五个中位数中取中位数，记为 。 的最小可能值是多少？
The integers from through are arbitrarily separated into five groups of numbers each. The median of each group is identified. Let equal the median of the five medians. What is the least possible value of
小提示：
一个五个数的组中位数不超过 ，至少需要该组有 个数不超过 。
A group median at most needs at least numbers at most
大提示：
若想让五个中位数的中位数很小，就需要至少三组都有较小的中位数。
Three small medians would require too many small numbers
视频讲解：
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文字解答：
如果某组的中位数至多为 ，那么这一组至少有 个数不超过 。若五个中位数的中位数至多为 ，则至少有 组满足这一点，需要至少 个不超过 的数，矛盾。因此 。这个下界可以达到，例如让五组的中位数为 ：、、、 和 。所以最小值是 。
If a group has median at most , then at least numbers in that group are at most . For the median of the five medians to be at most , at least groups would need such medians, requiring at least numbers at most , impossible. Thus . This is attainable, for example with group medians : use groups , , , , and . Hence the least possible value is .
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