Name: 【TED-Ed】你能解開假幣之謎嗎？- 詹妮弗-盧 (【TED-Ed】Can you solve the counterfeit coin riddle? - Jennifer Lu)
Uploaded: 2021-01-14T06:43:17.000Z
Duration: 4 min 35 s

You're the realm's greatest mathematician,

but ever since you criticized  the Emperor's tax laws,

你只有一支記號筆讓你記錄天數

But one day, you're suddenly brought before the Emperor

有一天，看起來比以往還生氣的皇帝

One of his twelve governors has been convicted of paying his taxes

which has already made its way into the treasury.

you've been granted a chance to earn your freedom by identifying the fake.

只要分辨出哪個是假的，你就有機會獲得自由

Before you are the twelve identical looking coins and a balance scale.

你前方有十二個長得一模一樣的錢幣和一個天秤

You know that the false coin will be very slightly lighter or heavier

你知道偽幣通常都比其他錢幣還要輕或重一點

before you'll be thrown back  into the dungeon.

You look around for anything else you can use,

你查看周圍是否有其他工具可以用

Pause here if you want  to figure it out for yourself!

如果你想自己想想看，請按暫停

Obviously you can't weigh each coin against all of the others,

很顯然你無法一個個硬幣分別秤重

so you'll have to weigh several coins at the same time

by splitting the stack  into multiple piles

then narrowing down  where the false coin is.

然後慢慢縮小條件找出偽幣在哪

Start by dividing the twelve coins into three equal piles of four.

將十二個硬幣平分成三堆各四個硬幣

Placing two of these on the scale gives us two possible outcomes.

將兩堆放在天平兩端，我們可以得出兩種可能的結果

If the two sides balance, all eight coins on the scale are real,

如果兩端平衡，上面八個硬幣就是真的

and the fake must be among  the remaining four.

假的就一定在剩下的四個硬幣中

So how do you keep track of these results?

Mark the eight authentic coins with a zero.

Now, take three of them and weigh them against three unmarked coins.

現在，拿起三個做好記號的硬幣與三個沒有記號的硬幣測量

If they balance, the remaining  unmarked coin must be the fake.

如果它們等重，剩下沒做記號的硬幣就是假的了

If they don't, draw a plus on the three unmarked coins if they're heavier

如果它們不等重，將較重沒做記號的硬幣畫加號，

Now, take two of the newly marked coins and weigh them against each other.

現在，將兩個新做上記號的硬幣互相秤重

如果等重，第三個硬幣便是假的

還有另一種方法，看他們的記號，

If they are plus coins,  the heavier one is the imposter.

如果是加號，比較重的一個就是偽造的

If they are marked with minus, it's the lighter one.

如果是減號，答案就是較輕的那一個

But what if the first two piles you weigh don't balance?

但如果從一開始兩堆的硬幣就不等重呢?

Mark the coins on the heavier side with a plus

將較重那一端的錢幣都畫上加號

and those on the lighter side  with a minus.

You can also mark the remaining four coins with zeros

since you know the fake one is already somewhere on the scale.

因為你知道假的硬幣就在天秤的某一端

so you can remove all remaining ambiguity in just two more weighings.

你要用剩下的兩次秤重排除疑惑得出結果

To do this, you'll need  to reassemble the piles.

One method is to replace three of the plus coins

and replace those  with three of the zero coins.

>From here, you have three possibilities.

If the previously heavier side of the scale is still heavier,

如果天秤上先前較重的那一端還是比較重

that means either the remaining plus coin on that side

or the remaining minus coin on the lighter side

就是剩下較輕那一端的減號硬幣

Choose either one of them, and weigh it against one of the regular coins

隨意選其中一個與正常的硬幣秤重

If the previously heavier side became lighter,

that means one of the three minus coins you moved

If they balance, the third is counterfeit.

如果它們等重，第三個就是偽造的

如果不等重，答案就是較輕的那一個

Similarly, if the two sides balanced after your substitution,

同樣地，如果你替換後兩端等重

then one of the three plus coins you removed

那其中三個加號硬幣當中就有一個

如果它們等重，第三個便是假的

如果不等重，那較重的那個就是假的

The Emperor nods approvingly at your finding,

and the counterfeiting Lord takes your place in the dungeon.

所以那個偽造大臣就接下了你在地牢裡的位置了