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解开没钱的朝拜者难题

Can you solve the penniless pilgrim riddle? - Daniel Finkel

“不是所有漫步之人都会迷路’’
‘’Not all those who wander are lost…’’
J.R.R 托尔金 《指环王之魔戒再现》
– J.R.R Tolkien. The Fellowship of the Ring
经过几个月的长途跋涉
After months of travel,
你终于到达了度沃尼亚
you’ve arrived at Duonia,
那座朝圣目的地
home to the famous temple
著名寺庙的所在地
that’s the destination of your pilgrimage.
你从西北侧进入
Entering from the northwest,
穿过城门 来到接待中心
you pass through the city gates and the welcome center,
你在那里会得到一张地图和一本小册子
where you’re given a map and a brochure.
地图显示该城有16个街区
The map reveals that the town consists of 16 blocks,
由五条从西到东的街道
formed by five streets thatrun west to east,
和五条从南到北贯穿的街道组成
intersecting five more that run north to south.
你面朝东 站在最北侧的那条街
You’re standing on thenorthernmost street facing east,
带大门的两个街区和接待中心都在你身后
with the two blocks containing the gate and the welcome center behind you.
寺庙的唯一入口在东南角
The temple’s only entrance liesat the very southeast corner.
步行距离并不远
It’s not a long walk,
但却有个问题
but there’s a problem.
你从小册子上得知
As you learn from the brochure,
度沃尼亚对所有游客要征收一种特殊的税
Duonia imposes a unique tax on all visitors,
他们到达城里的目的地时 必须要缴税
which must be paid when they arrive at their destination within the city.
税从零开始计算
The tax begins at zero,
每向东走一个街区 收两枚银币
increases by two silver for every block you walk east,
每向南走一个街区 收四枚银币
and doubles for every block you walk south.
但为了使税收更公平 根据最新的改革方案
However, a recent reform to make the tax fairer
每向北走一个街区 你的总账单减半
halves your total bill for every block you walk north
每向西走一个街区 减两枚银币
and subtracts two silver for every block you walk west.
只穿过大门到接待中心
Just passing through the gateand the welcome center
就意味着你已经欠了四枚银币
means you already owe four silver.
但作为朝拜者 你没有钱
As a pilgrim you carry no money
也没有办法赚到钱
and have no way of earning any.
而且 朝拜的规则是
What’s more, the rules of your pilgrimage
在你行走的过程中
forbid you from walking over any stretch of ground
禁止重复走过的路段
more than once during your journey—
但你可以横穿走过的路径
though you can cross your own path.
你能想出一个
Can you figure out a way
到达寺庙 而不用缴税
to reach the temple without owing any tax
或无论向任何方向走 都不重复走过的街区的办法吗?
or walking the same block twice in any direction?
如果你要自己想出办法 就在这里暂停
Pause here if you wantto figure it out for yourself.
数三下后公布答案:3
Answer in: 3
2
Answer in: 2
1
Answer in: 1
看看地图 考虑一下都有哪些选择
You look at the map to consider your options.
向寺庙方向走 税总是递增的
Walking towards the temple always increases the tax,
向寺庙的相反方向走 就递减
and walking away decreases it,
看上去好像如果不缴税的话 永远到不了
so it seems like you can never reach it without owing silver.
但要是绕着一个街区走会怎样呢?
But what happens when you walkaround a single block?
如果从欠四枚银币开始
If you start out owing four silver
向东顺时针走
and go clockwise starting east,
你的税单变成6枚 12枚 10枚 然后5枚银币
your tax bill becomes 6, then 12, then 10, then 5.
如果再绕一圈 你会欠7枚银币 14枚 12枚 然后是6枚银币
If you looped again, you’d owe 7, 14, 12, and 6.
看来每顺时针走一圈
It seems that each clockwise loop
你都要多欠一枚银币
leaves you owing one extra silver.
那逆时针转一圈会怎样呢?
What about a counterclockwise loop then?
还是从欠四枚银币开始 先向南走
Starting owing four again and going south first,
你的账单变成欠8枚 10枚 5枚 然后是3枚银币
your bill changes to 8, 10, 5 and 3.
再转一圈 就变成欠6枚 8枚 4枚然后是2枚银币
Looping again you’d owe six, eight, four, and two.
逆时针每转一圈 其实就挣一枚银币
Each counterclockwise loop actually earnsyou one silver.
那是因为每次乘以2的税
That’s because any tax doubled,
加上2 除以2 再减2
plus two, halved, and minus two,
最终得出的数都比开始时少1个
always ends up one smaller than it started.
这个问题的关键是
The key here is
尽管相反方向的不同税收
that while the different taxes for opposite directions
似乎可以相互抵消掉
may seem to balance each other out,
但它们运用的顺序
the order in which they’re applied
却能产生巨大不同
makes a huge difference.
你从欠4枚银币开始
You start off owing four silver,
那么逆时针循环四次会使欠费降到零
so four counterclockwise loops would get you down to zero.
可惜并没有那么简单
Unfortunately, it’s not that simple,
因为你不能重复走过的路线
since you can’t walk the same block twice.
但是还有另外的方法减掉账单
But there’s another way to reduce your bill:
那就是逆时针走一大圈穿过这座城市
walking one large counterclockwise loopthrough the city.
从起点开始 向南走三个街区
From your starting position,walk three blocks south.
你要避开最南端的那条街
You need to leave the southernmost street clear
把它留作最后的路段
for the final stretch,
继续逆时针方向 也就是向东
so continuing counterclockwisemeans going east.
走两个街区到东墙
Walk two blocks to the eastern wall
你就会欠一份巨款 36枚银币
and you owe a whopping 36 silver.
但现在你可以开始减少账单了
But now you can start reducing your bill.
向北过三条街 再向西走一条街 账单减到了2.5
Three blocks north and one block westcuts it to 2.5.
你不能从那里向西走
You can’t go west from there,
到那里就没路出去了
that would leave you with no way out.
所以要向南走一条街
So you go one block south,
再向西走剩下的三条街
and the remaining three blocks west,
这样你的账单就是负一银币
leaving you with a debt of negative one silver.
负数乘以二
And since doubling a negative number
还是负数
still gives you a negative number,
向南走三条街到南墙
walking the three blocks to the south wall
就意味着这城市欠你八枚银币
means the city owes you eight.
幸运的是那就足够
Fortunately, that’s exactly enough
让你穿过最后几条街到达寺庙了
to get you through the final blocks to the temple.
进去的时候 你会发现从朝拜之行中学到的东西:
As you enter, you realize whatyou’ve learned from your pilgrimage:
有时 间接路线才是到达目的地的最好的方法
sometimes an indirect route is the best way to reach your destination.
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If you enjoy our riddles,
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we think you’ll love the mind bugling brain teasing book
《数字小恶魔》
‘’The Number Devil’’
这归功于我们的合作伙伴Picador
And thanks to our partners at Picador.
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You can get a copy of this best seller
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at a major discount for a limited time.
查看一下留言区
Check the comment section,
或访问ed.ted.com/books了解更多信息吧
or visit ed.ted.com/books to learn more.

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译制信息
视频概述

“有时候间接路线才是到达目的地最好的方法”

听录译者

收集自网络

翻译译者

昵伊荙

审核员

审核员 V

视频来源

https://www.youtube.com/watch?v=6sBB-gRhfjE

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