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你能解开被盗的红宝石谜题吗? – 译学馆
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你能解开被盗的红宝石谜题吗?

Can you solve the stolen rubies riddle? - Dennis Shasha

正片结束后先不要离开 稍后有附加谜题
王国中一个最富有的商人
One of the kingdom’s most prosperous merchants
因进行腐败交易而被曝光
has been exposed for his corrupt dealings.
他几乎所有的财富都用来投资三十颗
Nearly all of his riches are invested in a collection of 30
珍贵的缅甸红宝石
exquisite Burmese rubies,
广场上的民众都高喊着要没收他的财产
and the crowd in the square is clamoring for their confiscation
以赔偿受害者
to reimburse his victims.
然而这个无良商人与他的同党
But the scoundrel and his allies at court
在法庭上陈述的证词非常有说服力
have made a convincing case that at least
就是他的财富至少有一部分是合法获取的
some of his wealth was obtained legitimately,
还为王室提供过优良服务
and through good service to the crown.
国王考虑了一分钟之后 宣布了对他的判决
The king ponders for a minute and announces his judgment.
因为没法获知这些宝石中有多少
Because there’s no way to know which portion of the rubies
是用贪污来的钱购买的
were bought with ill-gotten wealth,
因此惩罚就通过一个智力游戏决定
the fine will be determined through a game of wits
参与人是商人和国王最聪明的顾问——你
between the merchant and the king’s most clever advisor – you.
你们双方都提前获知了游戏规则
You’re both told the rules in advance.
商人先悄悄地将宝石分装在三个箱子里
The merchant will be allowed to discreetly divide his rubies
然后将这些箱子放到你的面前
among three boxes, which will then be placed in front of you.
你会收到三张卡片
You will be given three cards,
在将卡片分别放入箱子之前
and must write a number between 1 and 30 on each,
你要在每张上面写下1到30间的任一数字
before putting a card infront of each of the boxes.
随后三个箱子都会被打开
The boxes will then all be opened.
如果箱子里的宝石数不小于卡片上的数
For each box, you will receive exactly as many rubies as the number
那么 数字是几就得到几颗宝石
written on the corresponding card, if the box has at least that many,
但若卡片上的数字大于箱中实际宝石数
but if your number is greater than the number of rubies actually there,
商人则保留箱子中的全部宝石
the scoundrel gets to keep the entire box.
就商人如何分宝石 国王提出两个限定条件
The king puts just two constraints on how the scoundrel distributes his rubies.
每个箱子中至少装两颗宝石
Each box must contain at least two rubies
其中一个箱子要比另一个多装六颗
and one of the boxes must contain exactly six more rubies than another,
但你不知道它们是哪两个箱子
but you won’t know which boxes those are.
思考了几分钟后
After a few minutes of deliberation,
商人将宝石装好了
the merchant hides the gems,
箱子被拿到你的面前
and the boxes are brought in front of you.
你应该选择哪些数字
Which numbers should you choose
才能让这个商人罚款尽可能达到最大
in order to guarantee the largest possible fine for the scoundrel
并让受害者得到最多的赔偿
and the greatest compensationfor his victims?
如果你想自己思考一下 就先暂停视频
Pause the video now if you want to figure it out for yourself.
3 2 1
Answer in 3 Answer in 2 Answer in 1
你不想因为贪心把数字写得过大
You don’t want to overshoot by being too greedy.
但有一种方法可以确保你得到
But there is a way you can guarantee
商人手中超过一半的宝石
to get more than half of the scoundrel’s stash.
这种情况类似于国际象棋这种博弈性游戏
The situation resembles anadversarial game like chess –
只是你看不到对手出手
only here you can’t see theopponent’s position.
要想知道自己
To figure out the minimum number
最少能赢多少宝石
of rubies you’re guaranteed to win,
就需要先清楚最坏的情况
you need to look for the worst casescenario,
假设商人已经看清了你的路数
as if the merchant already knew your move
然后再放宝石 让你赢的最少
and could arrange the rubies to minimize your winnings.
你无法获知 哪个箱子宝石较多或较少
Because you have no way of knowing which boxes will have more or fewer rubies,
因此只能在三个卡片上写一样的数字
you should pick the same number for each.
假设你写了三个9
Suppose you write three 9’s.
商人可能将宝石分成8 14 8
The scoundrel might have allocated the rubies as 8, 14 and 8.
这时你能在中间的箱子里得到九颗
In that case, you’d receive 9
而在另两个中一无所获
from the middle box and no others.
另一种方法 可以确保你在两个箱子里
On the other hand, you can be sure that at least two boxes
都得到8颗以上宝石
have a minimum of 8 rubies.
接下来我们用反证法来证实
Here’s why. We’ll start by assuming the opposite,
两个箱子里最多只有7颗宝石
that two boxes have 7 or fewer.
这两个不会是宝石个数差为6的箱子
Those could not be the two thatdiffer by 6,
因为每个箱子中至少会有两颗宝石
because every box must have at least 2 rubies.
因此第三个箱子里
In that case, the third box would have
最多有13颗宝石——也就是7+6
at most 13 rubies—that’s 7 plus 6.
现在把三个箱子宝石数相加
Add up all three of those boxes,
结果平均数只有27
and the most that could equal is 27.
得出的数小于30 这个假设不成立
Since that’s less than 30, this scenario isn’t possible.
所以你现在可以知道 通过所谓的反证法
You now know, by what’s calleda proof by contradiction,
得出其中两个箱子里至少有八颗宝石
that two of the boxes have8 or more rubies.
如果你每张卡片上都写了8
If you ask for 8 from all three boxes
那么你至少能拿到16颗
you’ll receive at least 16—
这也是你所能保证的最好情况了
and that’s the best you can guarantee,
再次考虑 8 14 8这种情况就会明白
as you can see by thinking again about the 8, 14, 8 scenario.
你现在可以将超过半数的贪污款
You’ve recovered more than half thescoundrel’s fortune
赔偿给公众了
as restitution for the public.
尽管商人设法留住了 一些宝石
And though he’s managed to hold on to some of his rubies,
他的财富显然已经缩水了
his fortune has definitelylost some of its shine.
如果你对这个谜题很感兴趣 试试下面这道题
国王让你对弈另一个无良商人 这是一次全新挑战
这次你要将三十颗红宝石分成三份
商人选择并拿回其中两份
你怎样能得到最多宝石
这个附加谜题选自BRILLIANT网站
开始题目会比较简单 易于上手
随着难度的增加让玩家欲罢不能
帮助你想出多种方法解决遇到的棘手问题
锻炼思维敏捷度
点击进入BRILLIANT.ORG/TEDED网站
前833个人能使用这个链接
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你对自己的智商有信心吗?来看看这个视频,看看你能否解开这个谜题!

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视频来源

https://www.youtube.com/watch?v=2QJ2L2ip32w

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