Can you solve the honeybee riddle? - Dan Finkel

翻译人员: Carol Wang 校对人员: Candace Hwang

You’re a biologist on a mission

作为生物学家，

to keep the rare honeybee Apis Trifecta from going extinct.

你正在执行一项防止稀有蜜蜂 Apis Trifecta 绝种的任务。

The last 60 bees of the species are in your terrarium.

最后的 60 只蜜蜂 就在你的饲养室里，

You’ve already constructed wire frames of the appropriate size and shape.

你已构建了合适大小 和形状的巢框。

Now you need to turn them into working beehives

现在要把它们变成正常工作的蜂巢，

by helping the bees fill every hex with wax.

你需要往每个六边形里充蜡。

There are two ways to fill a given hex.

充蜡有两种方法：

The first is to place a bee into it.

第一种是放一只蜜蜂进去，

Once placed, a bee cannot be removed without killing it.

蜜蜂一旦放入便不能拿出， 除非杀死它；

The second:

第二种方法，

if at any point an unfilled hex has three or more neighboring wax-filled hexes,

如果一个空六边形与 三个以上充蜡的六边形相邻，

the bees already in the hive will move in and transform it.

蜂巢中的蜜蜂就会 进入该六边形充蜡。

Once the bees have transformed every hex in a hive,

一旦蜜蜂完成蜂巢里 所有六边形的充蜡，

you can place an additional bee inside and it’ll specialize into a queen.

你再放入一只蜜蜂， 它就会变成蜂王。

The hive, if well cared for, will eventually produce new bees

如果精心照料，

蜂巢就会产生新的蜜蜂， 将这个物种延续下去。

and continue the species.

If there are no hexes with three or more transformed neighbors,

如果没有与至少三个 充蜡六边形相邻的空六边形，

the bees will just sit and wait.

蜜蜂只能干等，

And once a bee transforms a hex, it can never become a queen.

而且充腊蜜蜂无法成为蜂王。

You could put 59 bees in one wire hive, wait till they transform all the hexes,

你可以把 59 只蜜蜂放入蜂巢框架， 等待它们为所有六边形充蜡后，

and then create a queen.

再创造一个蜂后。

But then just one collapse would end the species.

但只要一次失败， 就会导致该物种灭绝，

The more viable hives you can make now, the better.

所以，你现在制造的蜂巢越多越好。

So how many can you make with 60 bees?

那么 60 只蜜蜂能造多少个蜂巢呢？

Pause the video to figure it out yourself

[ 可暂停视频，自己解题 ]

Answer in 3

[ 答案倒计时 3 ]

Answer in 2

[ 答案倒计时 2 ]

Answer in 1

[ 答案倒计时 1 ]

Answer in 0

[ 答案倒计时 0 ]

What you're looking for here is some kind of self-sustaining chain reaction,

这里你需要用到的方法是 所谓的“自持链式反应”，

where a small number of bees will transform an entire hive.

只需少量蜜蜂即可完成蜂巢充蜡，

The lower the number of bees needed, the better.

需要的蜜蜂数量越少越好。

So how low can we go, and how can we engineer a chain reaction?

那最少需要多少只蜜蜂， 又如何设计链式反应呢?

就从第一个问题开始吧。

Let’s start with the first question.

There's a really clever approach to this,

有个非常巧妙的方法，

which involves counting the sides of the filled-in hexes,

那就是计算充蜡六边形的边数，

and examining their total perimeter.

并算出它们的总周长。

Let’s suppose we put bees in these three hexes.

假设把蜜蜂放在这三个六边形里，

The total transformed perimeter has 18 sides.

充蜡后的周长共有 18 条边。

But the middle hex has three transformed neighbors,

但中间的六边形 与三个已充蜡的相邻，

so the bees will transform it too.

所以，蜜蜂也会对它充蜡。

What happens to the perimeter?

现在周长是多少呢？

It’s still 18!

还是 18 !

And even after the bees transform the next sets of hexes with three neighbors,

即便蜜蜂完成下一轮 对三个充蜡邻居的六边形充蜡后，

it still won’t change.

周长依然不变。

What’s going on here?

这是什么道理呢？

Each hex that has at least three sides touching the bee-friendly space

至少有三个充蜡邻居的六边形 在蜜蜂完成充蜡后，

will remove those sides from the perimeter when it transforms.

相邻边要从周长中剔除，

Then it adds at most three new sides to the perimeter.

然后最多给周长增加三条新边。

So the perimeter of the transformed hexes will either stay the same or shrink.

因此，充蜡六边形的总周长 要么不变，要么变小。

The final perimeter of the entire hive is 54,

整个蜂巢的总周长是 54，

so the total perimeter of the hexes we place bees in at the start

所以，我们一开始放入蜜蜂，

must be at least 54 as well.

这些六边形的周长至少是 54 。

Dividing that 54 by the six sides on each non-adjacent hex

用 54 除以一个六边形边数 6，

tells us it’ll take at least 9 bees to transform the entire hive.

得出至少需要 9 只蜜蜂 才能完成整个蜂巢的充蜡。

That’s a great start,

这个开头不错，

but we still have the tough question of where the nine bees should go,

但棘手的问题是， 这 9 只蜜蜂该放哪里，

and if we’ll need more.

以及是否需要放入更多蜜蜂。

Let’s think smaller.

让我们想想小一点的蜂巢。

We already know that three bees could completely transform a hive this big.

我们已知 3 只蜜蜂 能完成这么大蜂巢的充蜡，

What about a slightly bigger one?

稍微大一点的蜂巢会怎样呢?

The perimeter of this hive is 30,

这个蜂巢的周长是 30，

which means we’ll need at least 5 bees to fill it in.

意味着我们至少需要 5 只蜜蜂完成充蜡。

With 6 it’d be easy.

6 只蜜蜂就轻松完成。

Placing them like this would fill out the whole hive in just three steps.

这样放置只需要三步 就能完成整个蜂巢充蜡。

But we can do better!

但我们可以做得更好！

We don’t actually need to place a bee on this hex,

其实勿需把蜜蜂放入该六边形，

since the other bees will transform that spot on their own.

因为其它蜜蜂会为它充蜡。

It looks like we have the beginning of a pattern.

看起来这个模式 有了一个良好的开端，

Can we extend it to our full hive?

能把它扩展到整个蜂巢吗？

That would mean placing our 9 bees like so.

即把我们的 9 只蜜蜂 都放在类似位置。

Once they get to work, they’ll create a chain reaction

一旦蜜蜂开始工作， 就会产生连锁反应，

that fills in the center of the hive and extend it to its edges.

直至填满蜂巢中心， 并延伸到蜂巢边缘。

Add a 10th bee to the completed hive and it becomes a queen.

在完工的蜂巢中放入第 10 只， 它就会变成蜂王。

Repeat that process five more times

重复这个过程五次，

and you’ve helped the last 60 members of Apis trifecta

你就帮最后的 60 只 Api trifecta 蜜蜂

create 6 producing hives.

建成了 6 个蜂巢。

All in all, it’s a pretty good bee-ginning.

总之，这个开端相当不错。