Name: 你能解開紅寶石被盜之謎嗎？- 丹尼斯-沙沙 (Can you solve the stolen rubies riddle? - Dennis Shasha)
Uploaded: 2021-01-14T08:39:37.000Z
Duration: 4 min 51 s

One of the kingdom's most prosperous merchants

進階被動語態

has been exposed for his corrupt dealings.

一系列共三十顆精緻 緬甸紅寶石的收藏品上，

要將這些紅寶石沒收 來償還他欠受害者的錢。

但這個惡棍和他在法庭上的盟友

But the scoundrel and his allies at court

說明他的財富至少 有一部分是合法取得，

國王沉思了一會兒， 宣佈了他的判決。

因為不可能知道 有多少比例的紅寶石

罰金將要透過 一個益智比賽來決定，

比賽是由這名商人對抗 國王最聰明的顧問——你。

兩位在賽前都已得知遊戲規則。

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

商人被允許可以私底下 將他的紅寶石

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

分別放入三個盒子中， 接著盒子會被放在你面前。

and the king's most clever advisor – you.

你必須要在每張卡片上寫下 1 到 30 之間的一個數字，

The merchant will be allowed to discreetly divide his rubies

接著在每個盒子前面 各放一張卡片。

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

你能從每個盒子得到的紅寶石數目

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

就是你寫在對應卡片上的數字。

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

前提是那個盒子中的 紅寶石要足夠。

但如果你的數字比盒子中 實際的紅寶石數目還多，

這個惡棍就可以保住整個盒子。

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

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

每個盒子要有 2 顆以上的紅寶石，

the scoundrel gets to keep the entire box.

其中一個盒子中的紅寶石數目必須 比另一個盒子多出 6 顆整——

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

Each box must contain at least two rubies

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

商人把寶石藏起來， 接著盒子被送到你面前。

but you won't know which boxes those are.

才能確保讓這個惡棍 被罰最高的罰金，

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

讓他的受害者得到最高額的補償？

若你想要嘗試自己解題， 請在這裡暫停。

in order to guarantee the largest possible fine for the scoundrel

and the greatest compensation  for his victims?

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

你不會想要因為太貪心 而讓數字超過。

這個惡棍必須要交出 他至少一半的藏匿物。

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

這個情況就類似 對抗遊戲，如西洋棋——

只是在這裡， 你看不到對手的位置。

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

若要得知你最少一定能 得到的紅寶石數目，

The situation resembles an  adversarial game like chess –

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

也就是當作商人 已經知道你要怎麼做，

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

他能夠安排紅寶石的分配， 來讓你贏得最少。

you need to look for the worst case scenario,

因為你不可能知道哪個盒子 有比較多／少紅寶石，

as if the merchant already knew your move

你應該對所有盒子 都選一樣的數字。

and could arrange the rubies  to minimize your winnings.

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

這個惡棍可以把紅寶石 分配成 8 顆、14 顆、8 顆。

you should pick the same number for each.

這麼一來，你只會從中間的盒子 得到 9 顆紅寶石，沒有其他的。

另一方面，你能確定 至少有兩個盒子

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

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

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

兩個盒子中的紅寶石 數目只有 7 顆或以下。

這兩個盒子的寶石數目 不可能相差 6 顆，

因為每個盒子都要有 2 顆以上的紅寶石。

Those could not be the two that  differ by 6,

會有至少 13 顆紅寶石——即 7+6。

because every box must have  at least 2 rubies.

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

現在，用所謂的反證法，你能知道

其中兩個盒子有至少 8 顆紅寶石。

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

如果你對每個盒子都索取 8 顆，

that two of the boxes have  8 or more rubies.

你能看出 這是你能做的最好保證，

若你能重新再想一次 8 顆、14 顆、8 顆的情境的話。

你取回了這個惡棍 一半以上的財富，

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

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

雖然他還是得以保住一些紅寶石，

他的財富肯定是失去了一些光芒。

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

his fortune has definitely  lost some of its shine.

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你能解開紅寶石被盜之謎嗎？- 丹尼斯-沙沙 (Can you solve the stolen rubies riddle? - Dennis Shasha)

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