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  • You're a biologist on a mission

    你是位生物學家,你的任務是

  • to keep the rare honeybee Apis Trifecta from going extinct.

    確保 Apis Trifecta 這種稀有蜜蜂不會絕種。

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

    這種蜜蜂的最後六十隻都在你的養育箱中。

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

    你已經做好了尺寸和形狀都很適當的線框稿。

  • Now you need to turn them into working beehives

    現在為了將它們轉變為可使用的蜂巢,

  • by helping the bees fill every hex with wax.

    你需要協助蜜蜂將六角形裝滿蜂蠟。

  • There are two ways to fill a given hex.

    給定一個六角形,有兩種方式可以裝滿它。

  • The first is to place a bee into it.

    第一:將一隻蜜蜂放在裡面。

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

    一旦把蜜蜂放進去,需要殺死牠才能移除牠。

  • The second:

    第二:

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

    如果在任何時點未裝滿的六角形,或至少有三邊鄰接到裝滿蠟的六角形,

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

    已經在蜂巢中的蜜蜂會移入,將之裝滿。

  • Once the bees have transformed every hex in a hive,

    一旦蜜蜂將蜂巢中所有的六角形都裝滿,

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

    你便可以再放一隻額外的蜜蜂進去,牠會成為女王。

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

    如果好好照顧蜂巢,最終它就會產生出新蜜蜂來,

  • and continue the species.

    讓這個物種延續。

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

    如果沒有任何六角形邊鄰接到三個以上裝滿的六角形,

  • the bees will just sit and wait.

    蜜蜂就會坐著等待。

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

    當一隻蜜蜂把一個六角形裝滿,牠就不可能成為女王。

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

    你可以把五十九隻蜜蜂放入蜂巢原型中,等牠們將所有的六角形裝滿,

  • and then create a queen.

    接著再創造一隻女王。

  • But then just one collapse would end the species.

    但只要一出狀況,整個物種就會滅亡。

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

    最好盡量做出更多可用的蜂巢。

  • So how many can you make with 60 bees?

    所以,你能用六十隻蜜蜂做出幾個蜂巢?

  • Pause the video to figure it out yourself

    請在此暫停以解題,答案即將公佈:

  • Answer in 3

  • Answer in 2

  • Answer in 1

  • Answer in 0

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

    在這裡,你要找的是一種自我維持的連鎖反應,

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

    讓少量的蜜蜂將整個蜂巢裝滿。

  • The lower the number of bees needed, the better.

    需要的蜜蜂數量越少越好。

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

    我們能把數量壓到多低?又要如何設計連鎖反應?

  • Let's start with the first question.

    我們先從第一個問題開始。

  • There's a really clever approach to this,

    有一個相當聰明的方法可以用,

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

    這個方法需要計算裝滿的六角形有多少個邊,

  • and examining their total perimeter.

    再計算它們的總邊長。

  • Let's suppose we put bees in these three hexes.

    假設我們把蜜蜂放在這三個六角形中。

  • The total transformed perimeter has 18 sides.

    被裝滿的六角形總共有十八個邊。

  • But the middle hex has three transformed neighbors,

    但中間的六角形有三邊鄰接到裝滿的六角形,

  • so the bees will transform it too.

    所以蜜蜂也會把這個六角形裝滿。

  • What happens to the perimeter?

    周長會如何?

  • It's still 18!

    仍然是十八!

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

    就算蜜蜂把後續其他有三邊鄰接的六角形也裝滿,

  • it still won't change.

    總邊長仍然不會變。

  • What's going on here?

    這是怎麼回事?

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

    任何六角形,只要至少有三邊接觸到對蜜蜂友善的空間,

  • will remove those sides from the perimeter when it transforms.

    在這些六角形被裝滿時,就會從總邊長中除去那幾個邊。

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

    接著最多會增加三條新的邊到總邊長當中。

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

    所以被裝滿的六角形的總邊長,若不是不變,就是變少。

  • The final perimeter of the entire hive is 54,

    整個蜂巢的最終總邊長是五十四,

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

    所以一開始,需要我們放蜜蜂進去的那些六角形,

  • must be at least 54 as well.

    總邊長必須至少是五十四。

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

    將五十四除以六個邊(每個不相鄰的六角形有六個邊)

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

    就可以知道我們至少需要九隻蜜蜂才能將整個蜂巢裝滿。

  • That's a great start,

    那是個好的開始,

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

    但我們仍然要解決一個難題:這九隻蜜蜂要放在哪裡?

  • and if we'll need more.

    還是我們需要不只九隻?

  • Let's think smaller.

    我們先想小一點。

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

    我們已經知道三隻蜜蜂可以把這麼大的蜂巢完全裝滿。

  • What about a slightly bigger one?

    那稍微大一點的呢?

  • The perimeter of this hive is 30,

    這個蜂巢的邊長是三十,

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

    那就表示我們至少需要五隻蜜蜂才能把它裝滿。

  • With 6 it'd be easy.

    有六隻就很容易。

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

    把蜜蜂像這樣放置,就能在三個步驟之後裝滿整個蜂巢。

  • But we can do better!

    但我們還能做得更好!

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

    我們並不需要在這個六角形當中放置蜜蜂,

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

    因為其他蜜蜂會靠牠們自己把這個六角形裝滿。

  • It looks like we have the beginning of a pattern.

    看起來,我們已經有了一種模式的開端。

  • Can we extend it to our full hive?

    我們能把它延伸到整個蜂巢嗎?

  • That would mean placing our 9 bees like so.

    這表示我們要將九隻蜜蜂這樣排列。

  • Once they get to work, they'll create a chain reaction

    當他們開始工作後,會製造一連串連鎖反應

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

    將蜂巢中央填滿,再延伸到邊緣。

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

    加入第十隻蜜蜂讓蜂巢完美,這只會變成女王。

  • Repeat that process five more times

    重複這個過程五次

  • and you've helped the last 60 members of Apis trifecta

    你就能幫助最後六十隻 Apis trifecta

  • create 6 producing hives.

    創造六個有生產力的蜂巢。

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

    總之,這會是很好的開端。

You're a biologist on a mission

你是位生物學家,你的任務是

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C2 高級 中文 蜂巢 裝滿 女王 反應 生產力 協助

Can you solve the honeybee riddle? - Dan Finkel

  • 1455 5
    林宜悉 發佈於 2020 年 10 月 24 日
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