Can you solve the counterfeit coin riddle? - Jennifer Lu

審譯者: Bruce Sung

You’re the realm’s greatest mathematician,

你是王國裏最偉大的數學家，

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

但由於批評國王的稅務法，

you’ve been locked in the dungeon with only a marker to count the days.

你被關進了大牢，

只能以筆劃線記日。

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

但有一天，你突然被帶到國王面前，

who looks even angrier than usual.

而國王看起來比往常更惱火。

One of his 12 governors has been convicted of paying his taxes

他十二名地方長官中的一個

被逮到用假金幣納稅，

with a counterfeit coin,

which has already made its way into the Treasury.

而這枚假金幣已經進到了金庫裏。

As the kingdom's greatest mathematician,

作爲王國裏最偉大的數學家，

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

你只要識別出假金幣， 就能重獲自由。

Before you are the 12 identical looking coins and a balance scale.

在你面前是十二個看起來 完全相同的金幣和一個天平。

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

你知道假金幣比其他的 要重或輕一點點。

But the emperor’s not a patient man.

但國王沒什麼耐性。

You may only use the scale three times

你只能用天平測量三次，

before you’ll be thrown back into the dungeon.

然後就會被關回大牢。

You look around for anything else you can use,

你向周圍尋找可以用的工具，

but there's nothing in the room, just the coins,

但屋子裏什麼也沒有，

只有金幣、天平、和你的筆。

the scale, and your trusty marker.

How do you identify the counterfeit?

你怎樣找出假金幣呢？

Pause now to figure it out yourself!

如果你想先自己想一想，在這按暫停！

Answer in 3

答案 3 秒之後會出現

Answer in 2

答案 2 秒後出現

Answer in 1

答案 1 秒後出現

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

顯然你不能把每個金幣都 和其他的一起比較重量，

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

所以你必須每次把金幣分成幾組，

by splitting the stack into multiple piles,

幾個金幣一起稱重，

then narrowing down where the false coin is.

縮小範圍直到找到假金幣。

Start by dividing the 12 coins into three equal piles of four.

先把十二枚金幣分成三堆四枚的。

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

在天平上放兩堆， 有兩種可能的情況。

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

如果天平兩邊平衡， 則這八枚金幣都是真的，

and the fake must be among the remaining four.

假的一定在另外四枚裏。

So how do you keep track of these results? That’s where the marker comes in.

你怎麼記錄這些結果呢？

就用你的筆。

Mark the eight authentic coins with a zero.

把八枚真金幣標上圓圈。

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

取三枚真金幣和三枚 沒有標記的金幣來比較重量。

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

如果平衡，那麼剩下的那枚 沒有標記的金幣一定是假的。

If they don’t, draw a plus on the three unmarked coins

如果不平衡，而且三枚 無標記的金幣比較重，就標上加號，

if they’re heavier, or a minus if they’re lighter.

如果它們比較輕，就標上減號。

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

現在把剛稱過的三枚金幣中的 兩枚放在天平兩端。

If they balance, the third coin is fake.

如果平衡，第三枚就是假的。

Otherwise, look at their marks.

否則，看這兩枚金幣的標記。

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

如果是加號， 那麽較重的那枚是假的。

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

如果是減號， 那麽較輕的那枚是假的。

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

但如果剛開始的兩堆金幣不平衡呢？

Mark the coins on the heavier side with a plus

把較重一邊的金幣標上加號，

and those on the lighter side with a minus.

較輕一邊的金幣標上減號。

You can also mark the remaining four coins with zeros,

你也可以將其他的四枚畫圈，

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

因為假金幣一定在稱過的八枚裏。

Now you'll need to think strategically

現在好好計劃一下，

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

在只再稱兩次的情況下找出答案。

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

你需要重新組合這堆金幣。

One method is to replace three of the plus coins

一種方法是把三枚加號金幣 換成減號金幣。

with three of the minus coins

and replace those with three of the zero coins.

再把那三枚減號金幣 換成畫圈的金幣。

From here, you have three possibilities.

這時有三種情況。

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

如果先前比較重的一邊仍然較重，

that means either the remaining plus coin on that side

那麽要麽是剩下的加號金幣比較重，

is actually the heavier one,

or the remaining minus coin on the lighter side is actually the lighter one.

要麽輕的那邊的減號金幣比較輕。

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

隨便選一個，和畫圈的金幣比較，

to see which is true.

來找到答案。

If the previously heavier side became lighter,

如果先前較重的一邊變輕了，

that means one of the three minus coins you moved is actually the lighter one.

意味著被移動的三枚減號金幣裏 有一枚比較輕。

Weigh two of them against each other.

把其中兩枚相比。

If they balance, the third is counterfeit.

如果平衡，第三枚就是假的。

If not, the lighter one is.

如果不平衡，輕的那枚就是假的。

Similarly, if the two sides balanced after your substitution,

相似地，如果兩邊在替換後平衡，

then one of the three plus coins you removed must be the heavier one.

那麽你移走的三枚加號金幣裏 有一枚比較重。

Weigh two of them against each other.

把其中兩枚相比。

If they balance, the third one is fake.

如果平衡，第三枚就是假的。

If not, then it's the heavier one.

如果不平衡，重的那枚就是假的。

The emperor nods approvingly at your finding,

國王對你的發現表示贊許，

and the counterfeiting lord takes your place in the dungeon.

而那名交了假金幣的官員 取代了你被關進地牢。