Can you solve the stolen rubies riddle? - Dennis Shasha

翻译人员: Ch'ng Tsu Pang 校对人员: Carol Wang

王国里有一位超级富商，

One of the kingdom’s most prosperous merchants

has been exposed for his corrupt dealings.

被爆涉及不法交易。

Nearly all of his riches

他将几乎全部身家

are invested in a collection

都兑换成了收藏品，

of 30 exquisite Burmese rubies,

就是 30 颗价值连城的缅甸红宝石，

and the crowd in the square

广场上聚集了大量百姓，

is clamoring for their confiscation

强烈要求没收宝石

to reimburse his victims.

以赔偿受害者。

But the scoundrel and his allies at court

奸商与法庭里的同谋串通，

have made a convincing case

成功证明

that at least some of his wealth

他至少有部分财富

was obtained legitimately,

是通过合法手段、

and through good service to the crown.

全心全意为国王服务所得。

The king ponders for a minute

国王寻思片刻，

and announces his judgment.

作出裁决：

Because there’s no way to know

因为无从得知

which portion of the rubies were bought with ill-gotten wealth,

哪些宝石是用不义之财买的，

the fine will be determined through a game of wits between the merchant

所以我决定通过斗智游戏 来决定该充公多少宝石，

与商人斗智的对手是 国王最聪明的参谋——你。

and the king’s most clever advisor – you.

You’re both told the rules in advance.

你和商人都事先知道了游戏规则，

The merchant will be allowed to discreetly divide his rubies

商人可以秘密地将宝石

among three boxes, which will then be placed in front of you.

分别装进三个箱子里， 再把箱子搬到你面前。

You will be given three cards,

然后，给你三张卡片，

and must write a number between 1 and 30 on each,

你必须在三张卡片上 分别写出 1 到 30 中的数字，

before putting a card in front of each of the boxes.

再将卡片分别放在三个箱子前，

The boxes will then all be opened.

然后，打开箱子。

For each box, you will receive exactly

如果你写的数字

as many rubies as the number written on the corresponding card,

等于或者少过箱中宝石的数量，

if the box has that many.

你就会拿到和该数字相同数量的宝石。

But if your number is greater than the number of rubies actually there,

但如果数字多过箱中宝石，

the scoundrel gets to keep the entire box.

则奸商得以留住整箱的宝石。

The king puts just two constraints on how the scoundrel distributes his rubies.

国王要求奸商遵守两个分宝石原则：

Each box must contain at least two rubies

每个箱子必须至少有两颗宝石，

and one of the boxes must contain exactly six more rubies than another—

且一个箱子的宝石数量必须 比另一个箱子多出六颗——

but you won’t know which boxes those are.

但你不知道到底是哪个箱子。

After a few minutes of deliberation,

只见奸商沉思了几分钟，

the merchant hides the gems, and the boxes are brought in front of you.

便将宝石分别藏好， 然后把箱子带到你眼前。

Which numbers should you choose

你应该写下什么数字

in order to guarantee the largest possible fine for the scoundrel

好让奸商得到最大的惩罚，

and the greatest compensation for his victims?

也让受害者得到最多的补偿呢？

Pause the video now if you want to figure it out for yourself.

[想尝试解题者，请暂停视频]

Answer in 3

[答案 3 秒后揭晓]

Answer in 2

[答案 2 秒后揭晓]

Answer in 1

[答案 1 秒后揭晓]

You don’t want to overshoot by being too greedy.

如果太贪心，可能会得不偿失，

But there is a way you can guarantee

但有一个方法可以保证你

to get more than half of the scoundrel’s stash.

至少获得奸商一半以上的赃物。

The situation resembles an adversarial game like chess –

这跟国际象棋类的对弈游戏很像——

only here you can’t see the opponent’s position.

只不过这里你看不到对手的出招。

To figure out the minimum number of rubies you’re guaranteed to win,

想算出至少可以稳获多少宝石，

you need to look for the worst case scenario,

你需要设想一下最糟的情况，

as if the merchant already knew your move

假设奸商已知道你会怎么做，

and could arrange the rubies to minimize your winnings.

而且能事先排好宝石， 把你的胜算降至最低。

Because you have no way of knowing which boxes will have more or fewer rubies,

因为你无从得知哪个箱子 宝石较多，哪个较少，

you should pick the same number for each.

你应该选择三个一样的号码。

Suppose you write three 9’s.

假设你写下三个 9，

The scoundrel might have allocated the rubies as 8, 14 and 8.

而奸商把宝石分成 8，14 和 8，

In that case, you’d receive 9 from the middle box and no others.

那么，你就只能取得 中间箱子的 9 颗宝石。

On the other hand, you can be sure that at least two boxes

而另一方面，你可以 确定至少有两个箱子

have a minimum of 8 rubies.

有至少 8 颗以上的宝石。

Here’s why.

原因如下：

We’ll start by assuming the opposite,

我们不妨从反面开始推想，

that two boxes have 7 or fewer.

若有两个箱子的宝石小于或等于 7 颗，

Those could not be the two that differ by 6,

则这它俩的宝石之差就不会是 6 颗，

because every box must have at least 2 rubies.

因为每个箱子至少会有 2 颗宝石。

In that case, the third box would have at most 13 rubies—that’s 7 plus 6.

这么一来，第三个箱子至多 有 13 颗宝石——也就是 7 加 6。

Add up all three of those boxes,

把这三个箱子的宝石数加起来

and the most that could equal is 27.

最多只能得到 27，

Since that’s less than 30,

也就是少于 30，

this scenario isn’t possible.

这是不可能发生的。

You now know, by what’s called a proof by contradiction,

通过这个反证法，

that two of the boxes have 8 or more rubies.

你得出有两个箱子 装有 8 颗或以上的宝石。

If you ask for 8 from all three boxes

只要三个箱子都写上 8，

you’ll receive at least 16—

那么你至少会得到 16 颗——

and that’s the best you can guarantee,

这也是你稳操胜券的最好结果，

as you can see by thinking again about the 8, 14, 8 scenario.

再次检视8，14，8的情形， 你的选择也是最好结果。

你已成功取回奸商半数以上的财产，

You’ve recovered more than half the scoundrel’s fortune

as restitution for the public.

并还之于民。

And though he’s managed to hold on to some of his rubies,

奸商纵使设法保住了一些宝石，

his fortune has definitely lost some of its shine.

但其财富无疑已大不如前了。