This one weird trick will get you infinite gold - Dan Finkel

翻译人员: Jiayi E 校对人员: Yanyan Hong

Well, you're in a real pickle.

好吧，你现在处于一个危险的困境。

You see, a few years ago, the king decided your life would be forfeit

就在前几年，国王决定要取你性命，

unless you tripled the gold coins in his treasury.

除非你能把他金库里的金币数量 翻三倍才能免你一死。

Fortunately for you, a strange little man appeared

幸运的是，一个奇怪的小老头出现了，

and magically performed the feat.

并神奇地助你完成了这一壮举。

He placed handfuls of coins in and out of a magical bag,

他一边将一把金币 放进一个神奇的袋子后再拿出来，

and sang a strange rhyme:

一边唱着一个奇怪的咒语：

“The more gold goes in and more comes out, as sure as I am me.

“就像‘我即是我’一样肯定， 金币放进越多，出来越多。

And in again, and out again, and now it’s it times three!”

再进去，再出来，现在翻了三倍！”

Incredibly, that tripled the coins and saved your life.

很不可思议， 那翻了三倍的金币救了你的性命。

Were you grateful? Yes. Were you desperate? Yes.

你感激吗？是的。 你很绝望吗？是的。

Did you promise him your first-born child in exchange for his help? Yes.

你有答应用你第一个孩子 作为他帮助的回报吗？是的。

Fast forward to today.

快进到现在，

No sooner have you given birth to a beautiful baby boy

就在你刚刚生了一个漂亮的男孩之后，

than the little man shows up to claim his prize.

那个小老头马上出现来领取他的奖励。

You cry and beg him not to take the baby.

你哭着求他不要带走你的宝贝，

Softening, he begins, “If you can guess my name—”

他心软了，他说： “如果你能猜出我的名字——”

“Banach-Tarski?” you say. “It’s on the front of your shirt.”

“巴娜科·塔司基？” 你答道， “就在你衣服上面写着”。

“What! That won’t do. Aha. My bag,” he explains,

“哈？那不算。啊哈，我的袋子。” 他解释到。

“increases the number of gold coins placed inside it in a very special way.

“里面有种很特殊的方法 可以增加放进去的金币的数量，

If I take any number of coins and place them in, more will come out.

我放进去任意数量的金币， 会拿出来更多的金币，

And if I place those in the bag again,

然后我把现在的这些金币 再放进去一遍，

the total that comes out will be three times whatever I began with.”

那么再拿出来的总数 总会是我第一次放进去的三倍。”

He takes 13 coins and places them in the bag,

他拿了 13 个金币放进了那个袋子，

then removes the contents.

然后把里面的东西拿了出来。

“I’ve used the magic once, not twice,” he says.

“我现在只用了一次魔法， 不是两次哦。”他说道。

“Tell me how many coins are in my hand and I’ll have mercy.”

“如果你能说出我手上 有多少金币，我就放过你。”

How many coins is he holding?

他拿着多少金币呢？

Pause here to figure it out yourself. Answer in 3

暂停一下，你自己来思考下。 倒计时 3

Answer in 2

倒计时 2

Answer in 1

倒计时 1

The bag’s magic works just like what in mathematics is called a “function,”

那个袋子的魔法原理 和数学上的“函数”一样，

and it’s convenient in both cases to use an arrow to denote the transformation.

在这两种情况下 都可以很方便的用箭头来表示这个转换，

We can write what we know like this.

我们可以像这样把我们知道写下来。

We want to know what goes in this particular blank.

我们想知道这个空白处该填入什么

Maybe the bag just multiplies the number of coins by some number.

或许这个袋子就是把金币的数量 乘上了某个数，

In that case, multiplying by that number twice

这样的话，乘这个数两次，

would be the same as multiplying by 3,

就等于原本的数量乘以 3 ，

which means the multiplier would be the square root of 3.

那这个乘数就应该是根号 3 。

That’s not a whole number, though.

不过，这就不是一个整数了，

And we don’t have bits of gold coins coming out of the bag.

而且那个袋子里出来的金币 可没有零碎的，

Something else is going on.

所以应该不是这个。

Well, if filling in the blank between 13 and 39 is too hard,

好吧，如果在 13 和 39 之间 填空太难的话，

maybe we can start with something easier.

那我们可以换个简单一点的，

Can we figure out what’ll happen to 1 coin?

我们能看出 从 1 枚金币开始是怎样的吗？

If you use the bag on a single coin twice, you end up with triple;

一枚金币进出这袋子两次， 你就会得到三倍的数量；

that’s three gold pieces.

也就是 3 枚金币。

Because the bag always increases the number of gold coins,

因为这个袋子总是会使金币的数量增加，

the blank must be between 1 and 3, so 2.

所以空白处必须是 在 1 和 3 之间，那就是2。

It’s a start. What’s next?

这算是个开始，那之后呢？

Let’s think about a few other possible starting places.

让我们看看其他几种可能，

We already know 2 becomes 3

我们都知道 2 会变成 3 ，

and that lets us fill in the next blank as well.

这可以帮助我们填写下一个空白处，

Now we’re getting somewhere!

这样我们就有了新的进展。

We just need to extend this out to 13.

我们只需要扩写到 13 ，

Remember the other rule, though:

但是还要记得另一条规则，

when you put more coins in, you get more coins out.

你拿出来的金币要比你放进去的多，

That means the numbers in every column must go in increasing order as well.

也就是说每列数字都必须是递增的。

In other words, because 6 coins become 9,

换种说法，因为 6 枚金币变成 9 枚，

it’s not possible for 4 coins to become 10.

那么 4 枚金币就不可能变成 10 枚，

Nor could 4 become 5, since 3 becomes 6.

而且因为 3 枚会变成 6 枚， 那么 4 枚也不可能变成 5 枚，

So 7 and 8 fill those blanks on the right of 4 and 5,

所以对应 4 和 5 的空白处 应该填入 7 和 8 ，

which in turn gives the answer for two more blanks.

这样就又可以推出 另外两个空白处的数字。

Knowing that the numbers go in increasing order in every column,

现在知道了每列数字都是递增的，

the only choices for the remaining blanks are 19, 20, 22, and 23.

那么剩下的空白处只能是 19 、 20 、22 和 23 。

And look! We have our answer!

看吧！我们得到了答案！

There must be 22 gold coins in his hand.

他手上肯定是 22 枚金币。

“I’ll give you three guesses,” the little man begins to say.

小老头说：“我可以给你三次机会。”

“22 coins,” you respond.

你回答道：“22个。”

“What?! How did you know?”

“哈？！你怎么知道？”

“I enjoy a good riddle,” you say. “Also, it’s on the back of your shirt.”

“我喜欢有意思的谜题”，你答道。 “而且，答案就在你衣服背面。”