2002 AMC 12A 第 9 题
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所有题目均经美国数学协会（MAA）官方合法授权使用。
9.
Jamal 想把 个电脑文件存到软盘上，每张软盘容量为 兆字节（MB）。其中三个文件各需要 MB，另有 个各需要 MB，剩下 个各需要 MB。一个文件不能拆分到多张软盘上。装下所有文件最少需要多少张软盘？
Jamal wants to store computer files on floppy disks, each of which has a capacity of megabytes (mb). Three of his files require mb of memory each, more require mb each, and the remaining require mb each. No file can be split between floppy disks. What is the minimal number of floppy disks that will hold all the files?
小提示：
所需总容量为 mb。
The total memory needed is mb
大提示：
放有一个 文件的软盘最多只能再放一个 文件，会浪费 mb；把这些浪费加起来。
A disk holding a file has room for only one file, wasting mb; add up this waste
解答：
文件总大小为 mb，所以仅按容量至少需要 张软盘。
含有 -mb 文件的软盘只能再放一个 -mb 文件，至少留下 mb 空间。三个 -mb 文件总共至少浪费 mb，超过半张软盘容量，因此至少需要 张。
十三张也足够：六张各放两个 -mb 文件，三张各放一个 -mb 文件和一个 -mb 文件，四张各放三个 -mb 文件。
因此，正确答案是 B。
The files need mb, so at least disks by volume alone.
A disk containing a -mb file has room for only one more -mb file, leaving at least mb unused. Across the three -mb files this wastes at least mb, over half a disk, forcing at least disks.
Thirteen suffice: six disks each hold two -mb files, three disks each hold one -mb file plus one -mb file, and four disks each hold three -mb files.
Thus, the correct answer is B.
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