锯竹（图）

Jenny · 发表于 2004-11-4 00:34:14

图中有等长的六枝毛竹。每枝节的长短不一。若只用一把锯子，锯六次要将它锯成十八段等长的竹段。该如何锯?

sean9991 · 发表于 2004-11-4 19:42:43

This question looks weird.

If only one bamboo stick is allowed to be cut each time, there is no way to cut them in six times. If more than one bamboo stick are allowed to be cut simultaneously, we need only 2 cuts.

Jenny · 发表于 2004-11-5 18:58:05

我刚看到这个题的时候，也很纳闷，要是把六根竹子绑在一起，只要锯两回就可以了。可干吗非要让锯六回呢？也许这道题就是这样设计的，就是让你锯六回，看能不能锯成

18段。下面是答案。

sean9991 · 发表于 2004-11-5 19:20:20

I think this is not a good question. Appearantly it did not rule out that more than one bamboo sticks can be cut at the same time. Then why there can't be more than two sticks at a time?

The answer is not good either. In that way, the resulting sticks are not identical. For any stick that is cut into three segments, the two on both end has one end flat and the other end sharp, while the middle segment has both ends sharp. Why not just align two sticks, assuming only two sticks can be cut at a time, and cut them at 1/3 of their length simultaneously?

husonghu · 发表于 2004-11-6 05:27:28

我想，此题的关键条件是没有尺子可量(虽然题中没明说)。这也是题目强调“每枝节
的长短不一”的原因(否则你就可用竹节当尺了)。若如此，所给的答案就是很巧妙
的了，尽管如sean9991所说，切口是斜的，但毕竟是等长的。

(我试着在不能用尺子量的条件下想答案，但没想到此法)。

但我感到迷茫的是为什么说是锯竹呢？锯木棒不成吗？

Jenny · 发表于 2004-11-7 01:27:12

good point!

sean9991 · 发表于 2004-11-9 00:37:33

I don't think so. Without any external help, how can you put the two equilateral triangles in the proper place to form the proper hexagon?

husonghu · 发表于 2004-11-9 23:13:02

get the proper hexagon without tools, only judged by naked eye.

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锯竹（图）

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Disagree with sean9991. 我的看法，此题是好题，答案很巧妙。

good point![:)]

Disagree! external help needed anyway

I agree with you -- it is only an approximation to