Can you solve the counterfeit coin riddle? - Jennifer Lu

校对人员: Gia Hwang

You’re the realm’s greatest mathematician,

你是王国里最伟大的数学家，

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

但因为批评皇帝的税法， 被关进了地牢，

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

你只能用一支记号笔划线记日。

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

但有一天，你突然被带到皇帝面前，

who looks even angrier than usual.

他看起来比往常更恼火。

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

证据表明，他的 12 位官员中，

有人用一枚假金币交了税，

with a counterfeit coin,

which has already made its way into the Treasury.

而这枚假币已进入宝库。

As the kingdom's greatest mathematician,

作为王国里最伟大的数学家，

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

你只要能辨出假币， 就有重获自由的机会。

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

你面前摆着 12 枚 一模一样的金币和一台天平，

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

你知道假币比其它的略重或轻一点，

But the emperor’s not a patient man.

但皇帝没什麽耐心，

You may only use the scale three times

在你被重新关回地牢前，

before you’ll be thrown back into the dungeon.

只有三次使用天平的机会。

You look around for anything else you can use,

你试图在周围寻找可用工具，

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

但屋子里什麽也没有——

只有金币、天平，

the scale, and your trusty marker.

还有忠实的记号笔。

How do you identify the counterfeit?

该怎样找出假币呢？

Pause now to figure it out yourself!

[可暂停以思考答案]

[答案倒计时：3]

Answer in 3

Answer in 2

[答案倒计时：2]

Answer in 1

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

显然，你无法把每个金币 依次与其它金币比对重量，

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

所以，必须把这些金币分组，

by splitting the stack into multiple piles,

几个金币一起称，

then narrowing down where the false coin is.

然后缩小范围找到假币。

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

先把 12 枚分成三堆四枚的，

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

在天平上放两堆，会有两种可能：

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

如果天平两边重量相等， 则这八枚金币都是真的，

and the fake must be among the remaining four.

假币一定在另外四枚里。

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

你如何记录这些结论呢？

记号笔就派上用场了。

Mark the eight authentic coins with a zero.

先把八枚真金币标上圆圈，

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

再取三枚真币 和三枚未标记的金币称重，

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

如果天平两边重量相等， 剩下的那枚无标记金币就是假的；

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

若重量不等，

三枚未标记金币重，就标上加号，

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

如果比较轻，就都标上减号。

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

取新标记的三枚金币中的两枚 放在天平上比对重量，

If they balance, the third coin is fake.

如果等重，那第三枚就是假的；

Otherwise, look at their marks.

否则，看这两枚金币的标记。

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

如果是加号，较重的那枚就是假的；

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

如果是减号，较轻的那枚就是假的。

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

如果一开始两堆金币重量不等呢？

Mark the coins on the heavier side with a plus

将较重一边的金币标上加号，

and those on the lighter side with a minus.

较轻一边的金币标上减号，

You can also mark the remaining four coins with zeros,

在其他的四枚上画圈，

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

因为假币就在称过的八枚里。

Now you'll need to think strategically

现在需要好好计划一下，

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

才能在称重两次的情况下找出假币，

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

为此，你需要重新组合这堆金币。

One method is to replace three of the plus coins

方法一是把三枚加号币换成减号币，

with three of the minus coins

and replace those with three of the zero coins.

同时在减号边补上三枚画圈的金币，

From here, you have three possibilities.

结果会有三种可能：

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

如果先前较重一边仍然较重，

that means either the remaining plus coin on that side

那么要么是剩下的加号币较重，

is actually the heavier one,

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

要么轻的那边的减号币较轻，

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

随便选一个，和画圈币比重量，

to see which is true.

来找到假币。

If the previously heavier side became lighter,

如果先前较重的一边变轻了，

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

说明替换的三枚减号币有一枚较轻。

Weigh two of them against each other.

比较其中的两枚，

If they balance, the third is counterfeit.

如果等重，第三枚就是假的；

If not, the lighter one is.

如果不等，轻的那枚就是假的。

Similarly, if the two sides balanced after your substitution,

以此类推，如果两边在替换后等重，

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

那么移走的三枚 加号币里有一枚较重。

Weigh two of them against each other.

比较其中的两枚，

If they balance, the third one is fake.

如果等重，第三枚就是假的；

If not, then it's the heavier one.

如果不等重，重的那枚就是假的。

The emperor nods approvingly at your finding,

皇帝点头赞许你的计谋，

and the counterfeiting lord takes your place in the dungeon.

而那名伪造金币的官员 则取代了你在地牢的位置。