Can you solve the birthday cake riddle? - Marie Brodsky

譯者: Yu-Chi Cheng 審譯者: Helen Chang

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

你朋友的生日就在明天，他即將滿

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

你忘了他的年紀。

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

你只知道他不只一歲，除此之外， 他看起來青春永駐。

You’d believe it if he was 2 or 200.

你確信他的年紀介於2歲到200歲之間。

The birthday boy is a giant,

這名生日男孩是一位巨人，

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

你非常擔心：如果他知道 你忘記了他的生日，

you'll become part of the feast.

你肯定會變成他的生日大餐。

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

糕點師傅已經為他精心準備了 一個小山大小的蛋糕，

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

而你的工作就是 雕刻蛋糕中央的巧克力歲數裝飾。

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

雖然你很想直接數蛋糕上的蠟燭，

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

但你實在太小隻， 沒辦法看到蛋糕的最上方。

Then you remember: the baker made an interior tunnel

然後你想起： 那位糕點師傅從內部做了一個

to activate the candles from below.

可以從蠟燭底部開關蠟燭的通道。

While the giant is asleep, you can sneak in,

趁巨人還在睡覺，你可以溜進通道，

count the candles and escape undetected.

把蠟燭數完一遍再逃走。

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

當夜幕降臨，你套上全身防護裝， 一頭鑽入香草奶油。

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

在通道內部你可以觀察到 蠟燭究竟是點著的還是熄滅的。

and can switch it on or off.

你更可以點燃或熄滅它。

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

有些現在就是亮著的，有些是熄滅的，

似乎沒有特定的規律。

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

這個通道是一個單一迴圈，因此， 從黑暗中你無法確認它的形狀與大小。

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

你並沒有攜帶任何東西， 在牆上做的任何記號也都會消失。

You need a strategy.

你需要一個策略。

How can you count the candles?

你要如何正確的數蠟燭數量?

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

[暫停影片思考一下，答案在3秒後]

Answer in 2

[答案在2秒後]

Answer in 1

[答案在1秒後]

There are a few ways to solve this problem.

很多種方法可以用來解決這個問題。

Let's start with the most straightforward.

讓我們從最直接的方法開始。

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

實際上，有一種方法 可以在通道內部做標記：

the state of the candle.

蠟燭的明暗狀態。

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

將第一個遇見的蠟燭設為點亮的狀態，

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

當你繼續向前走， 你總會看見另外一支點亮的蠟燭。

either a new one or you’re starting one.

可能是新的蠟燭 或是你遇見的第一支蠟燭。

The question is: how could you know which?

問題是：你要如何分辨？

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

第一個方式：熄滅你碰的第一個 亮的蠟燭，依原路返回。

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

返回的過程中， 要算出與過來時候相同的蠟燭數量。

If the starting candle is now off,

如果發現第一支蠟燭熄滅了，

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

你就完成了通道的迴圈， 成功地知道了巨人的年紀！

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

如果蠟燭還亮著，離開原處 直到你碰到下一支蠟燭，

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

看看是不是第一支蠟燭， 再重複上述步驟。

This will work... eventually.

這個方法最終會有效。

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

但如果這個巨人並不年輕， 很多蠟燭也早已被點亮，

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

你可能會像跑馬拉松一樣跑到白天。

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

你肯定不想在巨人吃蛋糕時還在裡面。

So let’s look for a more efficient solution.

所以我們來看看更有效率的方法。

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

如果是透過測試一系列假說 來猜測巨人的生日?

Suppose you guess he’s turning 10.

假設你猜巨人是10歲，

You could light the starting candle, walk forward 10,

你可以點亮起始點的那支蠟燭， 往前走到第10支蠟燭，

switch or leave the destination candle off, and return.

讓這支蠟燭熄滅著，回頭返程。

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

如果起始蠟燭仍然點燃著， 10歲就不是正確答案。

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

要是那支蠟燭是熄滅的， 10歲就可能是答案，

但你可能跑了不只一圈，

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

10的因數5與2也同樣有可能，

Then you would have passed a repeating pattern—

那麼，你看到的只是 初始狀態的重複罷了。

but that could have just been the starting arrangement.

So what if you changed the candles on the way?

那如果改變途中蠟燭的狀態呢？

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

如果把你經過的第一 到第十一支蠟燭全部點亮，

switch that off, then turn back,

接著熄滅掉第十一支，掉頭返回，

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

那麼第一個熄滅的蠟燭就會告訴你 實際蠟燭的數量。

And if you don't hit any extinguished candles,

要是途中都沒有碰到那支熄滅的蠟燭，

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

那你就會知道蠟燭的總數一定大於10。

You could then pick a larger guess and try again.

你就可以猜一個更大的數字， 然後再試一次。

To be systematic, you could increase your guess

為了更加系統化，每次在猜測時，

by the same number each time, say 4.

你可以增加相同的數字，比如 4。

If there were 99 candles,

假如總共有99根蠟燭，

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

這種方法需要 24 次往返 並涉及接觸到近 2,700 支蠟燭。

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

但你不需要線性的增加你的假設。

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

譬如，你可以猜雙倍的數目， 如10到20，再到40，

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

最終在你的第五趟旅程， 經過560支蠟燭，找到真正的蠟燭數。

Doubling allows you to reach high numbers quickly,

即便雙倍的假設能夠 讓你更快的接近更大的數目，

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

但你還是應該從較小的間隔開始， 以防止只有幾根蠟燭的情況。

After expecting a lengthy trek,

在經過漫長的路途後，

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

你高興地發現巨人只有12歲。

You hurry to change into slightly more inconspicuous clothing;

你趕緊換上較不起眼的衣服；

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

在巧克力上鑿下一些數字，

並許下一個願望：

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

希望你朋友吹蠟燭的時候， 自己不是站在下風處。