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# 1條好難的數學題!

首先講左,呢條係數學題,唔係IQ題,唔好同我想D唔知咩野答案

問題:呢度有12個,有其中一個係假的,你唔知佢重左定輕左,你有一個天砰,沒有刻度,也沒有法碼等東西。你只可以用天砰3次,就要找出那個波是假的,仲要知佢係輕左定重左。

我有小小提示:

首先,第一次一定唔會係左邊6個波,右邊6個波,因為如果左邊重左,但係你唔個假波係輕左定重左,所以你會唔知左邊定右邊先有假波,所以係唔可能的。

我想要的格式係。

一開始,分幾多組,左邊幾多個,右邊幾多個波,跟住如果平衡,你又會點,如果唔平衡,你又會點...................................

就係咁啦

問題:呢度有12個<<<波>>>,有其中一個係假的,你唔知佢重左定輕左,你有一個天砰,沒有刻度,也沒有法碼等東西。你只可以用天砰3次,就要找出那個波是假的,仲要知佢係輕左定重左。

打漏左

### 3 Answers

- 追求自由Lv 51 decade agoFavorite Answer
Step 1. Number the 12 balls by 1, 2, ..... 12;

Step 2. Put 1-4, 5-8 onto the beam balance;

The remaining steps will depend on the outcome of the beam balance.

I give one example: 1-4 heavier than 5-8

Step 3. Put 1,2,5 on one side and 3,4,6 on the other side ;

Case 1: Balance

Step 4. If balance, then weight 7 & 8. The lighter one is the fake one.

Case 2: Unbalance

Step 4. If unbalance (say 1,2,5 heavier than 3,4,6), weight 1 & 2.

Step 5: If balance, then 6 is lighter.

Step 5: If unbalance, then the heavier is the fake one.

- WaiLv 61 decade ago
The 12 balls are to be distributed into 3 groups respectively into A, B, C, each 4 balls. Assume that the fake ball is in B.

A-0000 B-0000 C-0000

Let's weigh A & C for the 1st time; if they are equal; you will find that the fake ball is in B. If we weigh A & B for the 2nd time, you will find that either A or B is lighter or heavier. Then, distribute the 4 balls of Group B into 2 parts, and weigh for the 3rd time. You will find that one part is heavier and the other part is lighter. Let's assume that the lighter part is with problem. So, we weigh the 2 balls on the scale to see which one is lighter. Then you will find one of them is the fake ball. However, we have to weigh the balls for 4 times instead of 3 times.

2008-05-15 21:32:56 補充：

Another method: to distribute, A with 5 balls, B with 2 balls, C with 5 balls.

1st time of weighing: to weigh A & C, if they are equal.

2nd time of weighing: then try B, one is heavier, the other is lighter.

3rd time of weighing: to weigh one ball of Group B, and one ball either from A or C,

2008-05-15 21:36:08 補充：

Then you will find out the fake one.

In conclusion, if A-0000, B-0000, C-0000, it will make at least 4 times of weighing, or more.

if A-00000, B-00, C-00000, it will make at least 3 times of weighing, or more.