Can you solve the birthday cake riddle? - Marie Brodsky

翻译人员: JIA Xinyue 校对人员: Helen Chang

Your friend’s birthday is tomorrow, and he’s turning...

你朋友的生日是在明天 他的岁数将是...

well... the issue is that you’ve forgotten.

额...问题是你已经忘记了

He’s older than 1, but beyond that, he looks timeless.

他超过1岁了，但是除此之外 他好像万寿无疆

You’d believe it if he was 2 or 200.

你完全相信他2岁或者200岁了

The birthday boy is a giant,

寿星是个巨人

and you're afraid that if your forgetfulness becomes known,

你害怕一旦他知道了你的健忘

you'll become part of the feast.

你就会变成他盛餐的一部分

The baker has meticulously prepared a small mountain range of a cake,

面包师精心准备了 一个像小山一样的的蛋糕

and your job is to sculpt the giant’s age as the chocolate centerpiece.

而你的工作就是把巨人的年龄 雕刻成巧克力的中心装饰

You would love to just count the candles on the cake,

你很想数一数蛋糕上的蜡烛

but you're much too small to see the top of it.

但是你太小了 根本看不到顶上的蜡烛

Then you remember: the baker made an interior tunnel

然后你想起来了： 面包师制作了一条内部隧道

to activate the candles from below.

为了从下面点亮蜡烛

While the giant is asleep, you can sneak in,

趁巨人睡着的时候，你可以溜进去

count the candles and escape undetected.

数一数蜡烛，然后悄悄逃走

As night sets, you pull on a full bodysuit and brace yourself for vanilla cream.

夜幕降临时，你穿上一套紧身衣 钻进香草奶油里

Anywhere in the tunnel, you can see whether the candle above you is lit,

在隧道的任何地方，你都可以看到 你上方的蜡烛是否被点亮

and can switch it on or off.

还可以点亮或者熄灭它

Some are currently on, and others off, in no discernible pattern.

现在有些蜡烛是点亮的 有些是熄灭的，没有明显的规律

The tunnel is a single loop, and in the dark you can’t tell its shape or size.

隧道是一个单环

在黑暗中无法分辨它的形状和大小

You aren’t carrying anything with you, and any marks you make will disappear.

你什么都没带 而且任何你做的标记都会消失

You need a strategy.

你需要想出一种策略

How can you count the candles?

你怎么数蜡烛？

Pause here to figure it out for yourself. Answer in 3

在这里停下来，自己想想 3秒后给出答案

Answer in 2

2秒后给出答案

Answer in 1

1秒后给出答案

There are a few ways to solve this problem.

有几种方法能解决这个问题

Let's start with the most straightforward.

让我们从最直接的开始

There’s exactly one way to mark a location in the tunnel:

恰有一种方法可以标记隧道中的位置：

the state of the candle.

依靠蜡烛的状态

You can mark the first candle you reach by lighting it or keeping it on.

你可以标记遇到的第一支蜡烛 点亮它或让它一直亮着

If you walk forward, you’ll eventually find another lit candle—

如果你向前走，你最终会找到 另一支点亮的蜡烛——

either a new one or you’re starting one.

要么是新的，要么是一开始那根

The question is: how could you know which?

问题是：你怎么能知道它是哪支？

Here’s one approach: turn it off and backtrack to the start

有一个方法：熄灭它，再由原路返回

by passing the same number of candles you passed on the way there.

走过和来的时候相同数量的蜡烛时

If the starting candle is now off,

如果起始蜡烛现在熄灭了

you’ve completed the loop and know the giant’s age!

那你就已经走完了环路 并且知道了巨人的年龄！

Otherwise, depart again, continuing until the next lit candle,

否则就再出发 直到下一支点亮的蜡烛

testing if it’s your starting one and so on.

验证它是不是起始蜡烛

如此循环往复

This will work... eventually.

这个方法到最后一定能成功

But if the giant isn’t young, and many candles are on,

但是如果巨人不年轻 而且很多蜡烛都亮着

you might have a marathon to run between now and sunrise.

从现在到日出 你可能要跑一场马拉松了

And you definitely don’t want to be in the cake when he starts digging in.

当他开始大吃特吃的时候 你肯定不想在蛋糕里

So let’s look for a more efficient solution.

所以让我们来找一个 更有效的解决方法

How about testing a series of hypotheses about the giant's age?

我们来猜这个巨人的年龄如何？

Suppose you guess he’s turning 10.

假设你猜他10岁了

You could light the starting candle, walk forward 10,

你可以点亮起始蜡烛，向前走10支

switch or leave the destination candle off, and return.

让到达的那支蜡烛熄灭着，然后返回

If the starting candle’s still on, 10 isn’t the answer.

如果开始的蜡烛还亮着 那么10就不是答案

If it’s off, 10 could be right, but you may have made multiple loops—

如果它是熄灭的，那10可能是对的

但是你可能循环不止一次

so 10′s factors 5 and 2 are also possibilities.

所以10的因子5和2也是可能的

Then you would have passed a repeating pattern—

接着你就会通过一个重复模式——

but that could have just been the starting arrangement.

但这可能只是开始的排列

So what if you changed the candles on the way?

如果你在路上换了蜡烛呢？

If you turned them all on while walking from candle 1 to 11,

如果你从1号蜡烛走到11号蜡烛时 把它们都点亮

switch that off, then turn back,

关掉它，然后走回去

the first unlit candle you find would tell you the exact candle count.

你找到的第一支熄灭的蜡烛 会告诉你确切的蜡烛数量

And if you don't hit any extinguished candles,

如果你没有遇到任何熄灭的蜡烛

you'll know that the total must be higher than 10.

那你该知道总数一定大于10

You could then pick a larger guess and try again.

然后你可以猜一个更大的数字 再次尝试

To be systematic, you could increase your guess

更有系统一点，你的每一个假设

by the same number each time, say 4.

可以增加相同的数字，比如4

If there were 99 candles,

如果一共有99支蜡烛

this method would take 24 roundtrips and involve visiting nearly 2,700 candles.

这种方法需要往返24次 需要经过近2700支蜡烛

But you don’t have to increase your guess linearly.

但你不需要线性地增加你的猜测

For instance, you could double it, from 10 to 20 to 40,

例如，你可以把它翻倍 从10到20到40

and discover the true number on your 5th trip after around 560 candles.

在你的第五次往返中，大约 560根蜡烛后，发现真正的数字

Doubling allows you to reach high numbers quickly,

翻倍可以让你快速达到较高的数值

while starting with small intervals in case there are only a few candles.

开始的时候间隔要小 以防只有几根蜡烛

After expecting a lengthy trek,

在预计可能要经历一次长途跋涉后

you’re pleased to discover the giant is only turning 12.

你很高兴发现这个巨人才12岁

You hurry to change into slightly more inconspicuous clothing;

你赶紧换上稍微不显眼的衣服

chisel up some enormous chocolate numbers; and at the party, make your own wish:

凿好巧克力数字 然后在派对上，许下你自己的愿望

that you’re not downwind when your friend blows out his candles.

当你朋友吹蜡烛的时候 你不在下风处