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假币谜题

Can you solve the counterfeit coin riddle? - Jennifer Lu

你是王国里最伟大的数学家
You’re the realm’s greatest mathematician,
但由于讽刺国王的税务法
but ever since you criticizedthe Emperor’s tax laws,
你被关进了大牢
you’ve been locked
以笔划线记日但一天
in the dungeon with only a marker to count the days.
你突然被带到国王面前
But one day, you’re suddenly broughtbefore the Emperor
而国王看起来比往常更恼火
who looks even angrier than usual.
他的十二个官员中的一个
One of his twelve governors has been convicted
用了假金币
of paying his taxes
来付了他的税
with a counterfeit coin
这枚加金币已经进到了宝库里
which has already made its wayinto the treasury.
作爲王国里最伟大的数学家
As the kingdom’s greatest mathematician,
你只要能识别出假金币 就能重获自由
you’ve been granted a chance to earn your freedom by identifying the fake.
在你面前是十二个看起来完全相同的金币和一个天平
Before you are the twelve identical looking coins and a balance scale.
你知道假金币
You know that the false coin
比其他的要重或
will be very slightly lighter or heavier
轻一点点
than the rest.
但国王没什麽耐心
But the Emperor’s not a patient man.
你只能用天平测量三次
You may only use the scale three times
然后就会被关回大牢
before you’ll be thrown backinto the dungeon.
你向周围寻找可以用的工具
You look around for anything elseyou can use,
但屋子里什麽也没有——
but there’s nothing in the room –
只有金币、 天平、
just the coins, the scale, and your trusty marker.
和你的笔你该怎样找出假金币呢?
How do you identify the counterfeit?
在这里暂停来自己思考答桉!
Pause here if you wantto figure it out for yourself!
答桉:
Answer in: 3
3答桉:
Answer in: 2
2答桉:
Answer in: 1
1显然你不能把每个金币都和其他的比一次
Obviously you can’t weigh each coinagainst all of the others,
所以你必须每次把金币分成几组
so you’ll have to weigh several coinsat the same time
几个金币一起称重
by splitting the stackinto multiple piles
缩小范围直到找到假金币
then narrowing downwhere the false coin is.
先把十二枚金币分成三堆四枚的
Start by dividing the twelve coins into three equal piles of four.
在天平上放两堆 有两种可能的情况
Placing two of these on the scale gives us two possible outcomes.
如果天平两边平衡
If the two sides balance,
则这八枚金币都是真的
all eight coins on the scale are real,
假的一定在另外四枚里
and the fake must be amongthe remaining four.
你怎麽记录这些结论呢?
So how do you keep track of these results?
就用你的笔
That’s where the marker comes in.
把八枚真金币标上圆圈
Mark the eight authentic coinswith a zero. Now,
取三枚真金币和三枚没有标记的金币称重
take three of them and weigh them against three unmarked coins.
如果平衡 那麽剩下的那枚没有标记的金币一定是假的
If they balance, the remainingunmarked coin must be the fake.
如果不平衡
If they don’t,
而且三枚没有标记的金币比较重
draw a plus on the three unmarked coins if they’re heavier
就标上加号如果它们比较轻
or a minus if they’re lighter. Now,
就标上减号现在把刚称
take two
过的三枚金币中的其中两枚在天平上称重
of the newly marked coins and weigh them against each other.
如果天平平衡 第三枚就是假的否则
If they balance, the third coin is fake. Otherwise,
看这两枚金币的标记
look at their marks.
如果是加号 那么较重的那枚是假的
If they are plus coins,the heavier one is the imposter.
如果是减号 那么较轻的那枚是假的
If they are marked with minus,it’s the lighter one.
但如果刚开始的两堆金币不平衡呢?
But what if the first two piles you weighdon’t balance?
把较重一边的金币标上加号
Mark the coins on the heavier sidewith a plus
较轻一边的金币标上减号
and those on the lighter sidewith a minus.
其他的四枚画圈
You can also mark the remaining four coinswith zeros
因为假金币一定在称过的八枚里
since you know the fake one is already somewhere on the scale. Now,
现在好好计划一下
you’ll need to think strategically
才能在再称两次的情况下找出答桉
so you can remove all remaining ambiguity in just two more weighings.
你需要重新组合这堆金币
To do this, you’ll needto reassemble the piles.
一种方法是把三枚加号金币
One method is to replacethree of the plus coins
换成减号金币
with three of the minus coins,
再把那三枚减号金币换成画圈的金币
and replace thosewith three of the zero coins.
这时有三种情况
>From here, you have three possibilities.
如果先前比较重的一边仍然较重
If the previously heavier side ofthe scale is still heavier,
那么要么是剩下的加号
that means either the remainingplus coin on that side
金币比较重
is actually the heavier one,
要么轻的那边的减号
or the remainingminus coin on the lighter side
金币比较轻
is actually the lighter one.
随便选一个
Choose either one of them,
和画圈的金币比较
and weigh it against one of the regular coins
来找到答桉
to see which is true.
如果先前较重的一边变轻了
If the previously heavier sidebecame lighter,
意味着被移动的三枚减号金币
that means one of the three minuscoins you moved
里有一枚比较轻
is actually the lighter one.
把其中两枚相比即可
Weigh two of them against each other.
如果平衡 第三枚就是假的
If they balance, the third is counterfeit.
如果不平衡 轻的那枚就是假的相似地
If not, the lighter one is. Similarly,
如果两边在替换后平衡
if the two sides balancedafter your substitution,
那么你移走的三枚加号金币
then one of the three plus coinsyou removed
里有一枚比较重
must be the heavier one.
把其中两枚相比
Weigh two of them against each other.
如果平衡 第三枚就是假的
If they balance, the third one is fake.
如果不平衡 重的那枚就是假的
If not, then it’s the heavier one.
国王点头对你的智商表示赞许
The Emperor nods approvinglyat your finding,
而那名交了假金币的官员代替了你在地牢里的位置
and the counterfeiting Lordtakes your place in the dungeon.

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