两个砝码

ob · 发表于 2006-4-7 22:44:06

N can be 16. Choose the 砝码 to be 3 and 8.
First time: 3, 5, 8
Second time: 2, 3, 5, 8
2, 3, 5, 8 can be used to measure weight from 1 to 16.

ob · 发表于 2006-4-8 03:05:12

You use the balance four times, which make the calculation more complicated. The topic allows you to use the balance for only thress times.

ob · 发表于 2006-4-8 03:06:50

I think you can only do addtion or subtraction. Use (2,8), you can not measure 1

ob · 发表于 2006-4-8 03:08:17

Welcome

ob · 发表于 2006-4-8 04:34:55

You are right

ob · 发表于 2006-4-8 04:54:01

This is more complicated than I though initially. For example use(3, 8):
First time: get 5, and you have 3, 5, 8
Second time: get 2, and you have 2, 3, 5, 8.
By using 2, 3, 5, 8, you can weigh any wieght from 1 to 16.

If you know the range of the weight of the rice, you can do the following to measure the weight from 17 to 21. But this may not match the requirement of the topic.
use (3,8) and first time get 3, you have 3,3,8
second time get 3, you have 3,3,3, 8.
Third time you can measure 17.

use (3, 8) and first time get 5, you have 3, 5, 8
second time get 5, you have 3, 5, 5, 8.
Third time you can measure 18.

use (3, 8) and first time get 5, you have 3, 5, 8
second time get 3, you have 3, 3, 5, 8.
Third time you can measure 19.

Similary, get 3,3,8,8 and you can measure 20
Get 3, 5, 8,8 or 3, 8, 8, 8 you can measure 21

ob · 发表于 2006-4-8 10:06:47

首先我们考虑一个1单位砝码，三次称重可以给出 1 到 7 单位大米。如下：

第一次，1单位砝码－－－－－－－－－－－－－－－－－－ 1 单位大米

第二次，1单位砝码＋ 1单位大米－－－－－－－－－－－－2 单位大米

第三次，1单位砝码＋ 1单位大米＋ 2单位大米－－－－－ 4 单位大米

1，2，4 组合，我们就可以给出 1 到 7 单位大米。---Is this the four time?

ob · 发表于 2006-4-8 10:14:16

9=8+3-2. Just one time. Put 8 and 3 on one side, put 2 on the other side and put the 9 units of rice. One condition, don't mix the rice together.

ob · 发表于 2006-4-8 10:29:46

Use 1 and 12, can not get 8?

ob · 发表于 2006-4-9 02:43:17

My mistake

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两个砝码

回复：两个砝码

回复：如果是这样，N 可以很大（可以证明 N 不会大于 91）

回复：回复：两个砝码

Welcome[@};-]

You are right[:P][@};-]

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回复：回复：回复：如果是这样，N 可以很大（可以证明 N 不会大于 91）

回复：说到底还是题目条件的含义模糊，可以用称出的米做砝码吗？称一次的严格标准是什么？

回复：17 可以

My mistake[:P]