【TED ED 中英雙語】 P79
Can you solve the penniless pilgrim riddle
你能解決身無分文的朝圣者之謎嗎
“流浪的人未必都迷茫......”?
? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ?——J.R.R 托爾金 《魔戒同盟》
After months of travel, you’ve arrived at Duonia, home to the famous temple that’s the destination of your pilgrimage.?
Entering from the northwest, you pass through the city gates and the welcome center, where you’re given a map and a brochure.?
The map reveals that the town consists of 16 blocks, formed by five streets that run west to east, intersecting five more that run north to south.
經(jīng)歷了數(shù)個月的旅程之后?你來到了多納。這里有一座著名的神殿，?也是你此次朝圣之旅的目的地。
你從西北方向進入該區(qū)域，穿過城門和游客中心，在這里你得到了?一份地圖和一個小冊子。
地圖顯示這個城鎮(zhèn)?由?16?個方塊區(qū)域構成，五條自西向東的大街， 與五條自北向南的大街彼此相交。
You’re standing on the northernmost street facing east, with the two blocks containing the gate and the welcome center behind you.
The temple’s only entrance lies at the very southeast corner.?
It’s not a long walk, but there’s a problem.?
As you learn from the brochure, Duonia imposes a unique tax on all visitors, which must be paid when they arrive at their destination within the city.?
The tax begins at zero, increases by two silver for every block you walk east, and doubles for every block you walk south.
你正位于最北邊的街道，面向東邊，在你身后是大門和 游客中心這兩個街區(qū)。
神殿的唯一入口位于城鎮(zhèn)的東南角。
去那里的路程并不長， 但有一個問題。
你從手冊中看到，多納對所有到訪者 都實行一種獨特的征稅制度，這項稅額在游客到達 城市內(nèi)某處目的地時收取。
稅額起初為零，每向東走一個街區(qū) 就增加兩個銀幣，每向南走一個街區(qū) 就使當前稅金翻倍。
However, a recent reform to make the tax fairer halves your total bill for every block you walk north and subtracts two silver for every block you walk west.
Just passing through the gate and the welcome center means you already owe four silver. As a pilgrim you carry no money and have no way of earning any.?
What’s more, the rules of your pilgrimage forbid you from walking over any stretch of ground more than once during your journey— though you can cross your own path.?
Can you figure out a way to reach the temple without owing any tax or walking the same block twice in any direction??
Pause here if you want to figure it out for yourself.?
Answer in: 3?
Answer in: 2
Answer in: 1
然而，最近的一項改革 使得繳稅更加公平，每向北走一個街區(qū)會使稅金減半，每向西走一個街區(qū) 就可以減掉兩個銀幣。
因為你已經(jīng)走過了大門和游客中心，你目前已經(jīng)欠下了?4?個銀幣。作為朝圣者， 你身無分文，也沒有辦法賺錢。
此外，朝圣有規(guī)定，禁止重復已經(jīng)走過的道路，但新的路線可以 與以前的路線相交。
你能夠想出不用交稅、 不重復走過的路線，就能到達神殿的方法么？
如果你想自己解題，請在此處暫停。
答案倒計時：
3
2
1
You look at the map to consider your options.?
Walking towards the temple always increases the tax, and walking away decreases it, so it seems like you can never reach it without owing silver.?
But what happens when you walk around a single block?
If you start out owing four silver and go clockwise starting east, your tax bill becomes six, then 12, then 10, then five.?
If you looped again, you’d owe seven, 14, 12, and six.
It seems that each clockwise loop leaves you owing one extra silver.
你看著地圖思考如何前進。
朝著神殿走總會增加稅金，背離神殿走則總會減少稅金，似乎你永遠也不能 零稅金到達神殿。
但如果你繞著單個街區(qū) 走一圈會發(fā)生什么呢？
如果你開始欠下?4?個銀幣 并且以順時針方向先向東走。
要交的稅金變成了?6?個銀幣，然后是?12?個銀幣，然后是?10?個銀幣，最后是?5?個銀幣。
如果你再走一圈， 你所欠的銀幣就是?7，14，12，6。
似乎每次順時針行走 會讓你多欠一個銀幣的稅。
What about a counterclockwise loop then??
Starting owing four again and going south first, your bill changes to eight, 10, five, and three.?
Looping again you’d owe six, eight, four, and two.
Each counterclockwise loop actually earns you one silver.?
That’s because any tax doubled, plus two, halved, and minus two, always ends up one smaller than it started.
The key here is that while the different taxes for opposite directions may seem to balance each other out, the order in which they’re applied makes a huge difference.
那逆時針走會怎么樣呢？
仍然以?4?個銀幣的稅金開始， 先向南走，稅金變成了?8，然后是?10，5，最后是?3。
再轉一圈，你欠的稅金變成?6，8，4，最后是?2。
每次逆時針行走 都會減少一個銀幣的稅金，
這是因為任何數(shù)字先翻倍，再加?2，再減半，然后再減?2，都會比原來的數(shù)字小?1。
關鍵在于， 稅金額度在相反方向上的差異似乎會相互抵消，但調(diào)整方向的先后順序 會產(chǎn)生很大不同。
You start off owing four silver, so four counterclockwise loops would get you down to zero.
Unfortunately, it’s not that simple, since you can’t walk the same block twice.?
But there’s another way to reduce your bill: walking one large counterclockwise loop through the city.?
From your starting position, walk three blocks south.?
You need to leave the southernmost street clear for the final stretch, so continuing counterclockwise means going east.?
Walk two blocks to the eastern wall and you owe a whopping 36 silver.
開始時你欠著?4?個銀幣，因此?4?次逆時針行走 就可以讓你繳納的稅金為?0?。
但這并沒有如此簡單， 因為你不能重復繞同一個街區(qū)兩次。
但還有一種方法 可以降低要繳納的稅金：在城市中走出一個大的逆時針圈。
從起始點開始向南走三個街區(qū)。你需要留出最南邊的街道 作為最后的路線，走逆時針路線意味著你要繼續(xù)向東。
向東走兩個街區(qū)到達城墻， 此時稅金達到了?36?個銀幣。
But now you can start reducing your bill.?
Three blocks north and one block west cuts it to 2.5.?
You can’t go west from here —that would leave you with no way out.?
So you go one block south, and the remaining three blocks west, leaving you with a debt of -1 silver.?
And since doubling a negative number still gives you a negative number, walking the three blocks to the south wall means the city owes you eight.
但從現(xiàn)在開始 你的稅金就要開始下降了。
向北走三個街區(qū)再向西走一個街區(qū) 使得稅金降至?2.5?。
你不能再繼續(xù)往西走， 不然就沒有路可以走了。
因此你繼續(xù)向南走一個街區(qū)， 再向西走三個街區(qū)，此時的稅金為?-1?個銀幣。
由于負數(shù)翻倍仍然是負數(shù)，向南走三個街區(qū) 意味著城市欠你?8?個銀幣。
Fortunately, that’s exactly enough to get you through the final blocks to the temple.?
As you enter, you realize what you’ve learned from your pilgrimage: sometimes an indirect route is the best way to reach your destination.
幸運的是，這些金幣的數(shù)量足夠讓你走到最后的神殿。
當你進入神殿時，你意識到 自己從這次朝圣中領會了一個道理：有時候，繞路才是 到達目的地的最好辦法。
