尺子整数刻度

ob · 发表于 2004-12-3 00:00:21

一把11厘米长的尺子，可否只刻3个整数刻度，即可用于量出1到11厘米之间的任何整数厘米长的物品长度？如果可以，问应刻哪几个刻度？

sean9991 · 发表于 2004-12-3 01:31:46

how many times are we allowed to use the ruler? only once?

ob · 发表于 2004-12-3 02:17:41

Only one time

sean9991 · 发表于 2004-12-3 03:37:19

The problem can be solved only when the object is guaranteed to have integer length. In this way, we can conclude that its length is 10 if it's shorter than 11 but longer than 9. Under this assumption, we can mark the ruler at 2, 7, and 8 centimeters.

ob · 发表于 2004-12-3 08:58:44

You are right for both your point and your answer!

也可以呀 · 发表于 2004-12-4 01:16:07

如果这样的话，在1、3、7处mark也可以呀?

husonghu · 发表于 2004-12-4 07:57:55

如果在相差为2cm之间的长度用“估”的话，则答案有多重。当然，sean9991的只要
一个(10cm)用“估”的，你的有两个要用“估”的。但这是100步与50步的差别。

如果不能用“估”的话，则此题无解. 因为3个刻度，加上两端，共5个刻度，最多
只能量10个长度: C(5,2)=10，总有一个没法量。

sean9991 · 发表于 2004-12-4 11:41:33

i thought the original problem is a little misleading. it's not just that there are multiple answers possible. actually, it also require a good estimation of the length to get the measurement right in one try. say the actual length is 6cm, how can we know which segment of the ruler should be used to measure it?

cba · 发表于 2004-12-7 02:36:58

只测量一次尚可以理解为不能分段或延长待测长度. 但是用"估"的办法有点成问题. 因为我可以在2,7cm处做两个刻度就够了.

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尺子整数刻度

question

Only one time

a little misleading

You are right for both your point and your answer!

回复：a little misleading

同意。

that's why

回复：that's why