IQ 題時間~ 是

ayako

早~~ 今日想同大家玩下IQ 題~

有12個波, 11個相同重量, 1個不同重量 (但不知是重D或輕D)
現有一個天秤, 只可以坪3次,
要找出邊一個波係唔同, 仲要知道埋重 or 輕

bubblesalt

Easy.....   

1) 5 on one side, 5 on the other, if it's equal then weight the other 2.
2) IF they are different then weight 2 and 2, same thing.
3) IF these are different then weight the last 2.

sike

can't think of one yet...

but bubblesalt's solution needs to include one more weighing to each scenario to determine the 仲要知道埋重 or 輕 part.  Therefore, the 3rd scenario will need a total of 4 weighs, which exceeded the limit.

ayako

Easy.....   

1) 5 on one side, 5 on the other, if it's equal then weight the other 2.
2) IF they ar ...
bubblesalt 發表於 2012-8-23 07:58

如sike 所說, 你的方法只可找出不同重量的一個, 但那不同的跟正常的比較, 是重了或是輕了呢? 請深述之, 謝謝.

B2L2

I tried this few years back, it is tricky.  Even remember the correct answer is hard and took me a while to figure it again.  Good luck.

Once you managed to solve this, try a similar one:

有13個波, 12個相同重量, 1個不同重量 (但不知是重D或輕D)
現有一個天秤, 只可以坪3次,
要找出邊一個波係唔同, (this time don't need to 知道埋重 or 輕)

ayako

I tried this few years back, it is tricky.  Even remember the correct answer is hard and took me a w ...
B2L2 發表於 2012-8-23 12:48

呢個都真係有d 難度... 唔........

快樂牛郎

took me 15 mins but I think I got it

bubblesalt

Oooooo  you have to find out if the 12th ball is lighter or heavier?

Ooops.. think think sin.

szasz

separate into 3 groups
each group with 4 balls (group abc)
let the unknown ball be xball

1. group a vs group b

if a>b then (proceed to 2)
if a=b then (proceed to 3)

2. that means xball is either in group a or group b (and we can use group c as standard balls)

3. that means group c has the xball

2.1 LET the heavy side BE H1234 & light side BE L1234

3.1 if group c has the xball (c1234) then

oh somebody already got the answer here

http://www.curiouser.co.uk/puzzles/12bsolution.pdf

2.2 we can either put

一輕兩重(left)對一輕兩重(right) (L1H1H2 vs L2H3H4)
and set L3L4 apart temporarily

if left side is heavier then
xball should be in either

兩重在左(H1H2)
or 一輕在右（L2）

(if equals then proceed to 4)
(if right side heavier proceed to 5)


THIRD WEIGHING
weigh the 2H among themselves: if equals then L is the xball. if one is heavier then it is the xball.

4. Either L3 or L4 is the xball. weigh L3 against L4. whichever is less heavy is the xball.

5. (L1H1H2 vs L2H3H4) right side heavier

that means x ball is in H3H4 & L1 ... 如此類推

同埋可以將一重三輕（left）對一輕三standard（right）

--- H1L1L2L3 vs L4＊＊＊ ---

如左重右輕即xball在 H1 & L4

obviously my maths isn't that good

如右重左輕即 L123入面有野，再(找其中兩個）互秤下，等，即第三個，不等，即較輕那個。（因為之前做左假設）

there is another way to do this with probability instead  ...

ayako

非常感謝你既參與呀~ 其實就咁睇你個答案都應該work, 以下係官方答案:

先將12個波分編號1,2,3...~12, 如果已知正常的就用x代表,以免混亂

step1:    1,2,3,4vs5,6,7,8
如果一樣，=>step2a
如果左邊重，即是1,2,3,4當中有一個重些 or 5,6,7,8有一個輕些
=>step2b﹙右邊重的話只要把觀念調轉來諗便可以﹚
----------------------------------------------------------------------------
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step2a:    已知道1-8是正常
            9,10,11vs xxx
如果一樣，=>step3a
如果唔同，=>step3b
----------------------------------------------------------------------------
------------------
step2b:     已知道9-12已是正常
1,2,5vs3,6,x
左邊重：1,2重些 or 6 輕些=>step3c
右邊重：3重些 or 5輕些=>step3d
一樣：4,7,8當中一個有問題=>step3e
----------------------------------------------------------------------------
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step3a:    9,10,11無問題的話就肯定是12有問題了。那麼只要再秤
            12 vs x
便知道12是重還是輕
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step3b:    從step2a已可知有問題的波是重還是輕﹙因xxx是正常的﹚，那麼只要再秤
            9 vs 10
如果一樣，便知道11有問題
如果唔同，也可從輕重知道9還是10有問題
----------------------------------------------------------------------------
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step3c:    1 vs 2
重的一個便有問題
如一樣，即是6是輕些的
----------------------------------------------------------------------------
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step3d:    3 vs x
唔同就是3重些
一樣就是5輕些
----------------------------------------------------------------------------
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step3e:    7 vs 8
輕的一個有問題
一樣就是4重些