It was a normal Tuesday at the superconductor, until a bug in the system created a small situation. Now your team is trapped in eleven separate pocket dimensions. Luckily for you, there’s a half-finished experimental teleportation robot that may be able to get you all home, if you can figure out how to work through the quirks of its design.
在超導體實驗室裡, 今天是平常的星期二, 直到系統中的一個錯誤 造成了一個小狀況。 現在你的團隊被困在 十一個不同的口袋異次元中。 你們很幸運,有一個半完成的 實驗性遠距傳送機器人 可能可以把大家帶回家, 但你得要想出如何運用它的設計。
Over interdimensional radio, your engineers explain that the robot can teleport into the alternate universes you’re trapped in, but it’ll do so completely at random. The robot has two levers and one big button. When it appears, you just switch the position of one of the levers from A to B or vice versa, and then the robot will note your dimensional position and teleport to another of the eleven dimensions at random. If it shows up again, you’ll have to pull a lever before it’ll teleport away. When anyone presses the button, the robot will bring everyone who pulled a lever back home. Anyone who didn’t will be lost in the multi-verse forever.
透過跨次元無線電, 你的工程師解釋說 機器人可以傳送到 你們受困的各個宇宙, 但傳送是完全隨機的。 機器人有兩根控制桿 和一個大按鈕。 當它出現時,你只要 把其中一根控制桿 從 A 切換到 B 或是反過來, 接著機器人就會 記下你的次元位置, 然後隨機傳送到 十一個次元中的另一個。 如果它再次出現,你得要再去拉 一根控制桿,它才會再次傳送走。 任何人只要按下按鈕, 機器人就會把有拉過 控制桿的人帶回家。 沒有拉過控制桿的人, 會永遠迷失在多重宇宙之中。
The challenge is to make sure everyone has pulled a lever before anyone hits the button. While you can talk to each other now over the interdimensional radio and agree on a plan, the robot’s teleportation technology will interfere with all attempts at communication once it arrives. You won’t be able to attach messages to the robot or scratch notes into its superstrong alloy body. Your only way to communicate information is to change the position of exactly one lever or hit the button.
挑戰之處在於要確保 大家都拉過控制桿, 然後才能按下按鈕。 雖然現在你們可以透過 跨次元無線電來跟彼此通話, 並訂定一個計畫, 但機器人的傳送技術 在機器人到達時會 干擾所有的通訊。 你無法讓機器人攜帶任何訊息, 它的合金身體超級堅硬 也無法在上面刻字。 你們之間只有一種交換資訊的方式, 就是拉控制桿或是按下按鈕。
What plan will make sure everyone gets home?
什麼樣的計畫能確保 大家都順利返家?
Pause the video now if you want to figure it out for yourself.
[如果你想要自己解題, 請在這裡將影片暫停。]
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It would be nice if you could set different combinations of the levers to indicate who’s already been visited by the robot. But it has only two levers. That gives four combinations— far too few to communicate about 11 people, especially when you’re forced to flip one to send the robot onward. There must be another way.
一個好點子是用不同的控制桿組合 來代表誰已經被機器人造訪過。 但只有兩根控制桿, 總共只能有四種不同的組合—— 完全不足夠代表十一個人, 何況你一定得要拉其中一根 控制桿才能讓機器人繼續傳送。 一定有其他的方法。
The critical insight is that not everyone has to know when every pocket dimension has been visited. If one person accepts responsibility ahead of time for hitting the button, then only they need to know who the robot has visited. In fact, they don’t even need to know exactly who’s been visited… just how many people have been.
關鍵的洞見在於, 並非每一個人都必須知道 何時每個口袋異次元 都已經被造訪過。 如果有一個人負責按下按鈕, 只有這個人需要知道 機器人造訪過誰。 事實上,他甚至不需要 確切知道誰被造訪過…… 知道有幾個人被造訪過就夠了。
You volunteer to be the person in charge of pressing the button when the moment is right, and give the following directions to everyone else. Your plan is simple: you’ll use the left lever to count visits, and the right lever will have no meaning, so there’s no harm in moving it up or down. Each of the others will pull the left lever from position A to position B exactly once. If the robot appears with the left lever already pulled down, or if an individual has previously pulled the left lever down at any point in the past, then they should move the right lever. You, meanwhile, will be the only one who ever resets the left lever from position B to position A. This gives you a way to count how many people have been visited by the robot. Everyone needs to pull the left lever down exactly once, and you’re the only one to pull it back up. So you know that the tenth time the robot visits you with its left lever in the down position, it must have visited all ten of the others. And that means you’re safe to press the button and teleport everyone home. It may take a while– most likely the robot will need to teleport around 355 times; but better that than leave anyone behind. Your teammates phase back into your home dimension one at a time. The mission proves a great success. Well...mostly.
你自願擔任在對的時機 按下按鈕的人, 並將下列指示傳達給每個人。 你的計畫很簡單:你會用 左控制桿來計算造訪次數, 右控制桿沒有意義, 所以拉動右控制桿不會造成傷害。 每一個人都只會把左控制桿 從 A 拉到 B 一次。 如果機器人出現時,左邊的 控制桿已經被拉下來到 B, 或者這個人過去任何時候 已經拉過一次左邊的控制桿, 他就要去拉右控制桿。 只有你一個人可以把左控制桿 從 B 拉回到 A。 這就讓你能夠計算有多少人 已經被機器人造訪過。 每一個人都只能拉 左邊的控制桿一次。 你是唯一能將它拉上來的人。 所以你會知道,當機器人造訪你時 左控制桿在下方位置的狀況 一共發生十次之後, 就表示機器人已經 造訪過所有十個人。 那就表示你可以安全地 按下按鈕,把大家傳送回家。 可能會花些時間—— 有可能機器人會需要 做 355 次傳送; 但那總比漏掉任何一個人要好。 你的團隊成員分階段一個一個 回到了你們的家鄉次元。 這個任務是個大成功。 嗯…大致上是啦。