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  • You heard the traveler's tales,

    你聽過旅行者的故事。

  • you followed the crumbling maps,

    你跟著殘缺不全的地圖。

  • and now, after a long and dangerous quest,

    而現在,經過漫長而危險的探索,

  • you have some good news and some bad news.

    你有一些好消息和一些壞消息。

  • The good news is you've managed to locate the legendary dungeon

    好消息是你已經成功找到了傳說中的地牢。

  • containing the stash of ancient Stygian coins

    貯藏著古代斯提亞人的錢幣。

  • and the eccentric wizard who owns the castle

    和擁有城堡的古怪巫師。

  • has even generously agreed to let you have them.

    甚至慷慨地同意讓你擁有它們。

  • The bad news is that he's not quite as generous

    壞消息是,他沒有那麼大度

  • about letting you leave the dungeon, unless you solve his puzzle.

    讓你離開地牢,除非你解決他的謎題。

  • The task sounds simple enough.

    這個任務聽起來很簡單。

  • Both faces of each coin bear the fearsome scorpion crest,

    每枚硬幣的兩面都有可怕的蠍子徽章。

  • one in silver,

    一個是銀色的。

  • one in gold.

    一個在黃金。

  • And all you have to do is separate them into two piles

    而你要做的就是把它們抽成兩堆。

  • so that each has the same number of coins facing silver side up.

    使每個人的硬幣數量相同,面向銀色的一面向上。

  • You're about to begin when all of the torches suddenly blow out

    你正準備開始的時候,所有的火把突然都熄滅了。

  • and you're left in total darkness.

    你就會陷入一片黑暗之中。

  • There are hundreds of coins in front of you

    你的面前有幾百個硬幣

  • and each one feels the same on both sides.

    而每一個人的兩邊感覺都是一樣的。

  • You try to remember where the silver-facing coins were,

    你試著回憶銀面幣在哪裡。

  • but it's hopeless.

    但它是無望的。

  • You've lost track.

    你已經失去了蹤跡。

  • But you do know one thing for certain.

    但有一件事你是知道的

  • When there was still light,

    當還有光亮的時候。

  • you counted exactly 20 silver-side-up coins in the pile.

    你數了數,正好有20枚銀色邊上的硬幣在堆裡。

  • What can you do?

    你能做什麼?

  • Are you doomed to remain in the dungeon with your newfound treasure forever?

    你是否註定要和你的新發現的寶藏永遠留在地牢裡?

  • You're tempted to kick the pile of coins

    你很想把那堆硬幣踢出去。

  • and curse the curiosity that brought you here.

    並詛咒把你帶到這裡的好奇心。

  • But at the last moment, you stop yourself.

    但在最後一刻,你阻止了自己。

  • You just realized there's a surprisingly easy solution.

    你才發現有一個出人意料的簡單解決方案。

  • What is it?

    什麼事?

  • Pause here if you want to figure it out for yourself.

    如果你想自己想明白的話,請在這裡暫停。

  • Answer in: 3

    答案:3

  • Answer in: 2

    答案:2

  • Answer in: 1

    答案:1

  • You carefully move aside 20 coins one by one.

    你小心翼翼地把20枚硬幣一個個挪到一邊。

  • It doesn't matter which ones: any coins will do,

    哪種無所謂:任何幣都可以。

  • and then flip each one of them over.

    然後把他們每個人都翻過來。

  • That's all there is to it.

    這就是全部的內容。

  • Why does such a simple solution work?

    為什麼這麼簡單的解決方案就能成功?

  • Well, it doesn't matter how many coins there are to start with.

    好吧,先不管有多少硬幣。

  • What matters is that only 20 of the total are facing silver side up.

    重要的是,總共只有20個面向銀色的一面。

  • When you take 20 coins in the darkness,

    當你在黑暗中拿了20個硬幣。

  • you have no way of knowing how many of these silver-facing coins

    你無從得知這些銀面錢幣的數量。

  • have ended up in your new pile.

    已經結束了在你的新堆。

  • But let's suppose you got seven of them.

    但我們假設你有七個人。

  • This means that there are thirteen silver-facing coins left

    這意味著還剩下十三枚銀面幣

  • in the original pile.

    在原來的一堆。

  • It also means that the other thirteen coins in your new pile

    這也意味著你新的那堆硬幣中的其他13個硬幣

  • are facing gold side up.

    是面向黃金的一面。

  • So what happens when you flip all of the coins in the new pile over?

    那麼,當你把新的一堆硬幣都翻過來的時候,會發生什麼?

  • Seven gold-facing coins and thirteen silver-facing coins

    7枚金面幣和13枚銀面幣。

  • to match the ones in the original pile.

    以配合原來那一堆的。

  • It turns out this works no matter how many of the silver-facing coins you grab,

    事實證明,無論你搶到多少銀面幣,這都是有效的。

  • whether it's all of them,

    是否是所有的人。

  • a few,

    一些。

  • or none at all.

    或根本沒有。

  • That's because of what's known as complementary events.

    這是因為所謂的互補事件。

  • We know that each coin only has two possible options.

    我們知道,每個硬幣只有兩種可能的選擇。

  • If it's not facing silver side up, it must be gold side up,

    如果不是面向銀色的一面朝上,那一定是金色的一面朝上。

  • and vice versa,

    反之亦然。

  • and in any combination of 20 coins,

    並在20枚硬幣的任意組合中。

  • the number of gold-facing and silver-facing coins

    金銀幣的數量

  • must add up to 20.

    必須加到20。

  • We can prove this mathematically using algebra.

    我們可以用代數在數學上證明這一點。

  • The number of silver-facing coins remaining in the original pile

    原堆中剩餘的銀面硬幣數量

  • will always be 20 minus however many you moved to the new pile.

    將永遠是20減去多少你移動到新的一堆。

  • And since your new pile also has a total of 20 coins,

    由於你的新堆也有總共20個硬幣。

  • its number of gold-facing coins will be

    其金面幣的數量將是。

  • 20 minus the amount of silver-facing coins you moved.

    20減去你移動的銀面幣數量。

  • When all the coins in the new pile are flipped,

    當新堆中的所有硬幣都被翻開時。

  • these gold-facing coins become silver-facing coins,

    這些金面幣變成了銀面幣。

  • so now the number of silver-facing coins in both piles is the same.

    所以現在兩堆銀面幣的數量是一樣的。

  • The gate swings open and you hurry away with your treasure

    大門一開,你就帶著你的寶藏匆匆離開了

  • before the wizard changes his mind.

    在巫師改變主意之前

  • At the next crossroads, you flip one of your hard-earned coins

    在下一個十字路口,你拋出一個你辛苦賺來的硬幣。

  • to determine the way to your next adventure.

    來決定你下一次冒險的方向。

  • But before you go, we have another quick coin riddle for you

    但在你走之前,我們還有一個快速的硬幣謎語給你--------。

  • one that comes from this video sponsor's excellent website.

    其中,來自這個視頻贊助商的優秀網站。

  • Here we have 8 arrangements of coins.

    這裡我們有8種錢幣的排列方式。

  • You can flip over adjacent pairs of coins as many times as you like.

    你可以隨意翻轉相鄰的硬幣對。

  • A flip always changes gold to silver, and silver to gold.

    一翻總是金變銀,銀變金。

  • Can you figure out how to tell, at a glance,

    你能不能想辦法分辨,一目瞭然。

  • which arrangements can be made all gold?

    哪些安排可以做到全金?

  • You can try an interactive version of this puzzle and confirm your solution

    您可以嘗試這個謎題的互動版本,並確認您的解決方案

  • on Brilliant's website.

    在Brilliant的網站上。

  • We love Brilliant.org because the site gives you tools

    我們愛Brilliant.org,因為這個網站給你提供了工具。

  • to approach problem-solving in one of our favorite ways

    用我們最喜歡的一種方式來解決問題------。

  • by breaking puzzles into smaller pieces or limited cases,

    通過將謎題分解成小塊或有限的案例。

  • and working your way up from there.

    並從那裡開始工作。

  • This way, you're building up a framework for problem solving,

    這樣,你就建立了一個解決問題的框架。

  • instead of just memorizing formulas.

    而不是隻記住公式。

  • You can sign up for Brilliant for free, and if you like riddles

    你可以免費註冊Brilliant,如果你喜歡猜謎語

  • a Brilliant.org premium membership will get you access

    成為Brilliant.org的高級會員後,您可以獲得以下服務

  • to countless more interactive puzzles.

    到無數的互動謎題。

  • Try it out today by visiting brilliant.org/TedEd

    今天就來試試吧,訪問 brilliant.org/TedEd。

  • and use that link so they know we sent you.

    並使用該鏈接,使他們知道我們給你發。

  • The first 833 of you to visit that link

    前833個訪問該鏈接的人。

  • will receive 20% off the annual premium subscription fee.

    將獲得年度高級訂閱費八折優惠。

You heard the traveler's tales,

你聽過旅行者的故事。

字幕與單字
自動翻譯

影片操作 你可以在這邊進行「影片」的調整,以及「字幕」的顯示

B1 中級 中文 美國腔 TED-Ed 硬幣 謎題 銀色 數量 解決

【TED-Ed】你能解出暗黑幣的謎題嗎? (Can you solve the dark coin riddle? - Lisa Winer)

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    Samuel 發佈於 2018 年 01 月 23 日
影片單字