Can you solve the counterfeit coin riddle

你能解决假币之谜吗

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You're the realm's greatest mathematician,

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

you've been locked in the dungeon

with only a marker to count the days.

你是王国里最伟大的数学家，

但由于讽刺国王的税务法，

你被关进了大牢

以笔划线记日。

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

who looks even angrier than usual.

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

with a counterfeit coin

which has already made its way into the treasury.

As the kingdom's greatest mathematician,

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

但一天，你突然被带到国王面前，

而国王看起来比往常更恼火。

他的十二个官员中的一个 用了假金币

来付了他的税。

这枚加金币已经进到了宝库里。

作爲王国里最伟大的数学家，

你只要能识别出假金币， 就能重获自由。

But the Emperor's not a patient man.

You may only use the scale three times

before you'll be thrown back  into the dungeon.

You look around for anything else you can use,

but there's nothing in the room -

just the coins,

the scale,

and your trusty marker.

How do you identify the counterfeit?

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

Answer in:3

Answer in:2

Answer in: 1

但国王没什麽耐心。

你只能用天平测量三次

然后就会被关回大牢。

你向周围寻找可以用的工具，

但屋子里什麽也没有——

只有金币、

天平、

和你的笔。

你该怎样找出假金币呢？

在这里暂停来自己思考答桉！

答案：3

答案：2

答案：1

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

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.

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

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

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

and the fake must be among  the remaining four.

显然你不能把每个金币都和其他的比一次，

所以你必须每次把金币分成几组，

几个金币一起称重，

缩小范围直到找到假金币。

先把十二枚金币分成三堆四枚的。

在天平上放两堆， 有两种可能的情况。

如果天平两边平衡， 则这八枚金币都是真的，

假的一定在另外四枚里。

So how do you keep track of these results?

That's where the marker comes in.

Mark the eight authentic coins with a zero.

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

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

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

or a minus if they're lighter.

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

If they balance, the third coin is fake.

Otherwise, look at their marks.

你怎麽记录这些结论呢？

就用你的笔。

把八枚真金币标上圆圈。

取三枚真金币和三枚没有标记的金币称重。

如果平衡，那麽剩下的那枚没有标记的金币一定是假的。

如果不平衡而且三枚没有标记的金币比较重，就标上加号，

如果它们比较轻，就标上减号。

现在把刚称过的三枚金币中的其中两枚在天平上称重。

如果天平平衡，第三枚就是假的。

否则，看这两枚金币的标记。

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

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

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

Mark the coins on the heavier side with a plus

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.

如果是加号，那么较重的那枚是假的。

如果是减号，那么较轻的那枚是假的。

但如果刚开始的两堆金币不平衡呢？

把较重一边的金币标上加号，

较轻一边的金币标上减号。

其他的四枚画圈，

因为假金币一定在称过的八枚里。

Now, you'll need to think strategically

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

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

One method is to replace  three of the plus coins

with three of the minus 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,

that means either the remaining plus coin on that side

is actually the heavier one,

or the remaining minus coin on the lighter side

is actually the lighter one.

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

to see which is true.

现在好好计划一下，

才能在再称两次的情况下找出答桉。

你需要重新组合这堆金币。

一种方法是把三枚加号金币换成减号金币。

再把那三枚减号金币换成画圈的金币。

这时有三种情况。

如果先前比较重的一边仍然较重，

那么要么是剩下的加号金币比较重，

要么轻的那边的减号金币比较轻。

随便选一个，和画圈的金币比较，

来找到答案。

If the previously heavier side became lighter,

that means one of the three minus coins you moved

is actually the lighter one.

Weigh two of them against each other.

If they balance, the third is counterfeit.

If not, the lighter one is.

Similarly, if the two sides balanced after your substitution,

then one of the three plus coins you removed

must be the heavier one.

Weigh two of them against each other.

If they balance, the third one is fake.

If not, then it's the heavier one.

The Emperor nods approvingly at your finding,

and the counterfeiting Lord takes your place in the dungeon.

如果先前较重的一边变轻了，

意味着被移动的三枚减号金币里有一枚比较轻。

把其中两枚相比即可。

如果平衡，第三枚就是假的。

如果不平衡，轻的那枚就是假的。

相似地，如果两边在替换后平衡，

那么你移走的三枚加号金币里有一枚比较重。

把其中两枚相比。

如果平衡，第三枚就是假的。

如果不平衡，重的那枚就是假的。

国王点头对你的智商表示赞许，

而那名交了假金币的官员代替了你在地牢里的位置。