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After months of travel, you've arrived at Duonia, home to the famous temple that's the destination of your pilgrimage.
经历了数个月的旅程之后，你来到了多纳，这里有一座著名的神殿，也是你此次朝圣之旅的目的地。
Entering from the northwest, you pass through the city gates and the welcome center, where you're given a map and a brochure.
你从西北方向进入该区域，穿过城门和游客中心，在这里你得到了一份地图和一个小册子。
The map reveals that the town consists of 16 blocks,
地图显示这个城镇由16个方块区域构成，
formed by five streets that run west to east, intersecting five more that run north to south.
五条自西向东的大街，与五条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.
你正位于最北边的街道，面向东边，在你身后是大门和游客中心这两个街区。
The temple's only entrance lies at the very southeast corner.
神殿的唯一入口位于城镇的东南角。
It's not a long walk, but there's a problem.
去那里的路程并不长，但有一个问题。
As you learn from the brochure, Duonia imposes a unique tax on all visitors,
你从手册中看到，多纳对所有到访者都实行一种独特的征税制度，
which must be paid when they arrive at their destination within the city.
这项税额在游客到达城市内某处目的地时收取。
The tax begins at zero, increases by two silver for every block you walk east, and doubles for every block you walk south.
税额起初为零，每向东走一个街区就增加两个银币，每向南走一个街区就使当前税金翻倍。
However, a recent reform to make the tax fairer halves your total bill for every block you walk north
然而，最近的一项改革使得缴税更加公平，每向北走一个街区会使税金减半，
and subtracts two silver for every block you walk west.
每向西走一个街区就可以减掉两个银币。
Just passing through the gate and the welcome center means you already owe four silver.
因为你已经走过了大门和游客中心，你目前已经欠下了4个银币。
As a pilgrim you carry no money and have no way of earning any.
作为朝圣者，你身无分文，也没有办法赚钱。
What's more, the rules of your pilgrimage forbid you from walking over any stretch of ground more than once during your journey
此外，朝圣有规定，禁止重复已经走过的道路，
though you can cross your own path.
但新的路线可以与以前的路线相交。
Can you figure out a way to reach the temple without owing any tax or walking the same block twice in any direction?
你能够想出不用交税、不重复走过的路线，就能到达神殿的方法么？
You look at the map to consider your options.
你看着地图思考如何前进。
Walking towards the temple always increases the tax, and walking away decreases it,
朝着神殿走总会增加税金，背离神殿走则总会减少税金，
so it seems like you can never reach it without owing silver.
似乎你永远也不能零税金到达神殿。
But what happens when you walk around a single block?
但如果你绕着单个街区走一圈会发生什么呢？
If you start out owing four silver and go clockwise starting east, your tax bill becomes 6, then 12, then 10, then 5.
如果你开始欠下4个银币并且以顺时针方向先向东走，要交的税金变成了6个银币，然后是12个银币，然后是10个银币，最后是5个银币。
If you looped again, you'd owe 7, 14, 12, and 6.
如果你再走一圈，你所欠的银币就是7，14，12，6。
It seems that each clockwise loop leaves you owing one extra silver.
似乎每次顺时针行走会让你多欠一个银币的税。
What about a counterclockwise loop then?
那逆时针走会怎么样呢？
Starting owing four again and going south first, your bill changes to 8, 10, 5, and 3.
仍然以4个银币的税金开始，先向南走，税金变成了8，然后是10，5，最后是3。
Looping again you'd owe 6, 8, 4, and 2.
再转一圈，你欠的税金变成6，8，4，最后是2。
Each counterclockwise loop actually earns you one silver.
每次逆时针行走都会减少一个银币的税金，
That's because any tax doubled, plus two, halved, and minus two, always ends up one smaller than it started.
这是因为任何数字先翻倍，再加2，再减半，然后再减2，都会比原来的数字小1。
The key here is that while the different taxes for opposite directions may seem to balance each other out,
关键在于，税金额度在相反方向上的差异似乎会相互抵消，
the order in which they're applied makes a huge difference.
但调整方向的先后顺序会产生很大不同。
You start off owing four silver, so four counterclockwise loops would get you down to zero.
开始时你欠着4个银币，因此4次逆时针行走就可以让你缴纳的税金为0。
Unfortunately, it's not that simple, since you can't walk the same block twice.
但这并没有如此简单，因为你不能重复绕同一个街区两次。
But there's another way to reduce your bill: walking one large counterclockwise loop through the city.
不过还有一种方法可以降低要缴纳的税金：在城市中走出一个大的逆时针圈。
From your starting position, walk three blocks south.
从起始点开始向南走三个街区。
You need to leave the southernmost street clear for the final stretch, so continuing counterclockwise means going east.
你需要留出最南边的街道作为最后的路线，走逆时针路线意味着你要继续向东。
Walk two blocks to the eastern wall and you owe a whopping 36 silver.
向东走两个街区到达城墙，此时税金达到了36个银币。
But now you can start reducing your bill. Three blocks north and one block west cuts it to 2.5.
但从现在开始你的税金就要开始下降了。向北走三个街区再向西走一个街区使得税金降至2.5。
You can't go west from here -- that would leave you with no way out.
你不能再继续往西走，不然就没有路可以走了。
So you go one block south, and the remaining three blocks west, leaving you with a debt of -1 silver.
因此你继续向南走一个街区，再向西走三个街区，此时的税金为-1个银币。
And since doubling a negative number still gives you a negative number,
由于负数翻倍仍然是负数，
walking the three blocks to the south wall means the city owes you eight.
向南走三个街区意味着城市欠你8个银币。
Fortunately, that's exactly enough to get you through the final blocks to the temple.
幸运的是，这些金币的数量足够让你走到最后的神殿。
As you enter, you realize what you've learned from your pilgrimage: sometimes an indirect route is the best way to reach your destination.
当你进入神殿时，你意识到自己从这次朝圣中领会了一个道理：有时候，绕路才是到达目的地的最好办法。
