Can you solve the counterfeit coin riddle

你能解決假幣之謎嗎

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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.

你是王國里最偉大的數(shù)學家，

但由于諷刺國王的稅務法，

你被關(guān)進了大牢

以筆劃線記日。

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，你突然被帶到國王面前，

而國王看起來比往常更惱火。

他的十二個官員中的一個 用了假金幣

來付了他的稅。

這枚加金幣已經(jīng)進到了寶庫里。

作爲王國里最偉大的數(shù)學家，

你只要能識別出假金幣， 就能重獲自由。

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

但國王沒什麼耐心。

你只能用天平測量三次

然后就會被關(guān)回大牢。

你向周圍尋找可以用的工具，

但屋子里什麼也沒有——

只有金幣、

天平、

和你的筆。

你該怎樣找出假金幣呢？

在這里暫停來自己思考答桉！

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.

顯然你不能把每個金幣都和其他的比一次，

所以你必須每次把金幣分成幾組，

幾個金幣一起稱重，

縮小范圍直到找到假金幣。

先把十二枚金幣分成三堆四枚的。

在天平上放兩堆， 有兩種可能的情況。

如果天平兩邊平衡， 則這八枚金幣都是真的，

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.

你怎麼記錄這些結(jié)論呢？

就用你的筆。

把八枚真金幣標上圓圈。

取三枚真金幣和三枚沒有標記的金幣稱重。

如果平衡，那麼剩下的那枚沒有標記的金幣一定是假的。

如果不平衡而且三枚沒有標記的金幣比較重，就標上加號，

如果它們比較輕，就標上減號。

現(xiàn)在把剛稱過的三枚金幣中的其中兩枚在天平上稱重。

如果天平平衡，第三枚就是假的。

否則，看這兩枚金幣的標記。

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.

如果是加號，那么較重的那枚是假的。

如果是減號，那么較輕的那枚是假的。

但如果剛開始的兩堆金幣不平衡呢？

把較重一邊的金幣標上加號，

較輕一邊的金幣標上減號。

其他的四枚畫圈，

因為假金幣一定在稱過的八枚里。

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.

現(xiàn)在好好計劃一下，

才能在再稱兩次的情況下找出答桉。

你需要重新組合這堆金幣。

一種方法是把三枚加號金幣換成減號金幣。

再把那三枚減號金幣換成畫圈的金幣。

這時有三種情況。

如果先前比較重的一邊仍然較重，

那么要么是剩下的加號金幣比較重，

要么輕的那邊的減號金幣比較輕。

隨便選一個，和畫圈的金幣比較，

來找到答案。

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.

如果先前較重的一邊變輕了，

意味著被移動的三枚減號金幣里有一枚比較輕。

把其中兩枚相比即可。

如果平衡，第三枚就是假的。

如果不平衡，輕的那枚就是假的。

相似地，如果兩邊在替換后平衡，

那么你移走的三枚加號金幣里有一枚比較重。

把其中兩枚相比。

如果平衡，第三枚就是假的。

如果不平衡，重的那枚就是假的。

國王點頭對你的智商表示贊許，

而那名交了假金幣的官員代替了你在地牢里的位置。