You’re overseeing the delivery of crucial supplies to a rebel base deep in the heart of enemy territory. To get past Imperial customs, all packages must follow a strict protocol: if a box is marked with an even number on the bottom, it must be sealed with a red top.
你負責監管將重要補給品 遞送到反抗軍基地的過程, 基地位在敵人領土 深處的心臟地帶。 若要通過帝國的海關,所有的包裹 都要遵循一項嚴格的協定: 如果箱子的底部標記了偶數數字, 它就必須要用紅色的蓋子來封裝。
The boxes are already being loaded onto the transport when you receive an urgent message. One of the four boxes was sealed incorrectly, but they lost track of which one. All the boxes are still on the conveyor belt. Two are facing down: one marked with a four, and one with a seven. The other two are facing up: one with a black top, another with a red one.
在箱子全被放上運輸交通工具後, 你才收到一則緊急訊息。 四個箱子中有一個的封裝不正確, 但他們已經無法追蹤是哪一個。 所有的箱子都還在輸送帶上。 兩個箱子被反過來放: 一個標記了「4」, 另一個標記了「7」。 另外兩個箱子是正著放的: 一個是黑色箱蓋, 另一個是紅色箱蓋。
You know that any violation of the protocol will get the entire shipment confiscated and put your allies in grave danger. But any boxes you pull off for inspection won’t make it onto this delivery run, depriving the rebels of critically needed supplies. The transport leaves in a few moments, with or without its cargo. Which box or boxes should you grab off the conveyor belt?
你知道只要違反了協定 就會讓整批貨被沒收, 還會讓盟友陷入危險。 若你把某個箱子拿下來查驗, 它就趕不上這次遞送, 反抗軍就得不到迫切需要的補給品。 運輸交通工具馬上就要離開了, 不論有沒有貨都會開走。 你應該從輸送帶上取下 哪一個或哪幾個箱子?
Pause the video now if you want to figure it out for yourself! Answer in: 3 Answer in: 2 Answer in: 1
如果你想要試著自己解題, 請在這裡暫停! 答案即將公佈:3 答案即將公佈:2 答案即將公佈:1
It may seem like you need to inspect all four boxes to see what’s on the other side of each. But in fact, only two of them matter.
看起來似乎你會需要 查驗所有四個箱子, 看看每個箱子的另一面是什麼。 但,事實上,當中 只有兩個才是要緊的。
Let’s look at the protocol again. All it says is that even-numbered boxes must have a red top. It doesn’t say anything about odd-numbered boxes, so we can just ignore the box marked with a seven. What about the box with a red top? Don’t we need to check that the number on the bottom is even? As it turns out, we don’t. The protocol says that if a box has an even number, then it should have a red top. It doesn’t say that only boxes with even numbers can have red tops, or that a box with a red top must have an even number. The requirement only goes in one direction. So we don’t need to check the box with the red lid. We do, however, need to check the one with the black lid, to make sure it wasn’t incorrectly placed on an even-numbered box.
咱們來再看一次協定。 它只有說,偶數數字的箱子 需要用紅色箱蓋。 它沒有提到奇數數字的 箱子要如何處理, 所以我們可以忽略 標記為「7」的箱子。 那麼紅色箱蓋的箱子呢? 我們不需要確認一下 它底下的數字是不是偶數嗎? 結果發現,的確不需要。 協定說,如果箱子是偶數數字, 它就應該用紅色箱蓋。 它並沒有說只有標記 偶數數字的箱子才能用紅色箱蓋, 也沒說紅色箱蓋的箱子一定 得是標記偶數數字的箱子。 要求是單向的。 所以我們不用去檢查 紅色箱蓋的箱子。 然而,我們確實需要檢查 黑色箱蓋的那個箱子, 來確保沒有不小心將黑色箱蓋 蓋在偶數數字的箱子上。
If you initially assumed the rules imply a symmetrical match between the number on the box and the type of lid, you’re not alone. That error is so common, we even have a name for it: affirming the consequent, or the fallacy of the converse. This fallacy wrongly assumes that just because a certain condition is necessary for a given result, it must also be sufficient for it. For instance, having an atmosphere is a necessary condition for being a habitable planet. But this doesn’t mean that it’s a sufficient condition – planets like Venus have atmospheres but lack other criteria for habitability.
如果你一開始就假設 這些規則意味著箱子上的數字 和箱蓋的類型之間有著 對稱的配對,你並不孤單。 那種錯誤非常常見, 它甚至被起了個名字: 肯定後件, 或是相反謬誤。 這種謬誤是一種錯誤假設, 誤認為當某一個條件 必然會導致某個結果時, 光是有它就足以導致這個結果。 比如,「有大氣」是星球適合居住的 必要條件。 但這並不表示有這個條件就充分了。 像金星也有大氣, 但它缺乏其他居住條件。
If that still seems hard to wrap your head around, let’s look at a slightly different problem. Imagine the boxes contain groceries. You see one marked for shipment to a steakhouse and one to a vegetarian restaurant. Then you see two more boxes turned upside down: one labeled as containing meat, and another as containing onions. Which ones do you need to check? Well, it’s easy – make sure the meat isn’t being shipped to the vegetarian restaurant, and that the box going there doesn’t contain meat. The onions can go to either place, and the box bound for the steakhouse can contain either product.
如果你仍然覺得很難懂, 咱們來看一個不太一樣的問題。 想像這些箱子中放的是食品雜貨。 你看到一個箱子上寫著 要運送到一間牛排屋, 另一個箱子則是要 運送到素食餐廳。 接著你又看到兩個 反過來放的箱子。 其中一個標示著內有肉品, 另一個則是內有洋蔥。 你需要檢查哪一個? 嗯,這很容易, 確保肉品不要被運送到素食餐廳, 以及運送到素食餐廳的 那個箱子中沒有肉品。 洋蔥運送到這兩個地方都沒關係, 要運送到牛排屋的箱子 也可以裝這兩種食品。
Why does this scenario seem easier? Formally, it’s the same problem – two possible conditions for the top of the box, and two for the bottom. But in this case, they’re based on familiar real-world needs, and we easily understand that while vegetarians only eat vegetables, they’re not the only ones who do so. In the original problem, the rules seemed more arbitrary, and when they’re abstracted that way, the logical connections become harder to see.
為什麼這個情境似乎就容易多了? 形式上,它也是同樣的問題—— 箱蓋有兩種可能的條件, 箱底也有兩種。 但在這個例子中,這些條件 是根據真實世界的需求來設計, 我們很容易了解素食者只吃蔬菜, 而吃蔬菜的人不只有素食者。 原始問題的規則似乎隨意許多, 當它們被抽象化成那樣時, 會比較難看出當中的邏輯連結。
In your case, you’ve managed to get enough supplies through to enable the resistance to fight another day. And you did it by thinking outside the box – both sides of it.
在你的情況中,你得以 讓足量的補給品通關, 使得反抗軍能再繼續奮戰。 而你能辦到,就是因為 你的思考能跳脫箱子—— 它的兩面。