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One of the kingdom's most prosperous merchants has been exposed for his corrupt dealings.
王国里有一位超级富商，被爆涉及不法交易。
Nearly all of his riches are invested in a collection of 30 exquisite Burmese rubies,
他将几乎全部身家都兑换成了收藏品，就是30颗价值连城的缅甸红宝石，
and the crowd in the square is clamoring for their confiscation to reimburse his victims.
广场上聚集了大量百姓，强烈要求没收宝石以赔偿受害者。
But the scoundrel and his allies at court have made a convincing case
奸商与法庭里的同谋串通，
that at least some of his wealth was obtained legitimately, and through good service to the crown.
成功证明他至少有部分财富是通过合法手段、全心全意为国王服务所得。
The king ponders for a minute and announces his judgment.
国王寻思片刻，作出裁决。
Because there's no way to know which portion of the rubies were bought with ill-gotten wealth,
因为无从得知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 and the king's most clever advisor -- you.
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。
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 among three boxes, which will then be placed in front of you.
商人可以秘密地将宝石分别装进三个箱子里，再把箱子搬到你面前。
You will be given three cards, and must write a number between 1 and 30 on each, before putting a card in front of each of the boxes.
然后，给你三张卡片，你必须在三张卡片上分别写出1到30中的数字，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 as many rubies as the number written on the corresponding card, if the box has that many.
如果你写的数字等于或者少过箱中宝石的数量，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, the scoundrel gets to keep the entire box.
但如果数字多过箱中宝石，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 and one of the boxes must contain exactly six more rubies than another
每个箱子必须至少有两颗宝石，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, the merchant hides the gems, and the boxes are brought in front of you.
只见奸商沉思了几分钟，便将宝石分别藏好，然后把箱子带到你眼前。
Which numbers should you choose in order to guarantee the largest possible fine for the scoundrel and the greatest compensation for his victims?
你应该写下什么数字好让奸商得到最大的惩罚，也让受害者得到最多的补偿呢？
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 to get more than half of the scoundrel's stash.
但有一个方法可以保证你至少获得奸商一半以上的赃物。
The situation resembles an adversarial game like chess -- only here you can't see the opponent's position.
这跟国际象棋类的对弈游戏很像--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, you need to look for the worst case scenario,
想算出至少可以稳获多少宝石，你需要设想一下最糟的情况，
as if the merchant already knew your move and could arrange the rubies to minimize your winnings.
假设奸商已知道你会怎么做，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, you should pick the same number for each.
因为你无从得知哪个箱子宝石较多，哪个较少，你应该选择三个一样的号码。
Suppose you write three 9's. The scoundrel might have allocated the rubies as 8, 14 and 8.
假设你写下三个9。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 have a minimum of 8 rubies.
而另一方面，你可以确定至少有两个箱子有至少8颗以上的宝石。
Here's why. We'll start by assuming the opposite, that two boxes have 7 or fewer.
原因如下。我们不妨从反面开始推想，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, because every box must have at least 2 rubies.
则这它俩的宝石之差就不会是6颗，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, and the most that could equal is 27.
把这三个箱子的宝石数加起来最多只能得到27。
Since that's less than 30, this scenario isn't possible.
也就是少于30，这是不可能发生的。
You now know, by what's called a proof by contradiction, that two of the boxes have 8 or more rubies.
通过这个反证法，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 you'll receive at least 16
只要三个箱子都写上8，那么你至少会得到16颗，
and that's the best you can guarantee, as you can see by thinking again about the 8, 14, 8 scenario.
这也是你稳操胜券的最好结果，再次检视8，14，8的情形，你的选择也是最好结果。
You've recovered more than half the scoundrel's fortune as restitution for the public.
你已成功取回奸商半数以上的财产，并还之于民。
And though he's managed to hold on to some of his rubies, his fortune has definitely lost some of its shine.
奸商纵使设法保住了一些宝石，但其财富无疑已大不如前了。
