Can you solve the Billy Bonka riddle? - Edwin F. Meyer · TED-Ed
进入神秘糖果实验室，面对Billy Bonka的逻辑游戏，通过观察和推理找出自己的发色。适合练习逻辑推理和英语理解。
You’re on a tour of the eccentric Billy Bonka’s mysterious candy factory,
你正在参观古怪的比利·邦卡（Billy Bonka）那座神秘的糖果工厂。
when a wrong turn searching for the restroom lands you in the TOP SECRET candy laboratory.
当你为了寻找洗手间而走错方向时，竟然意外闯入了那个属于“绝密级”的糖果实验室……
Enraged at your trespassing, Bonka explains that the consequences are simple: you must play his game.
邦卡对你擅自闯入的行为感到愤怒，并解释说后果很简单：你必须按照他的规则来“玩游戏”。
You win, he’ll set you free.
你赢了，他会放你自由的。
You lose, he’ll throw you into his Chew-O-Meter 3000.
如果你输了，他就会把你扔进他的“Chew-O-Meter 3000”（一种用于测量咀嚼力的设备）里。
and you’re as good as gum.
你简直一无是处（或：你毫无价值）。
Bonka unveils his latest invention: candies that instantly change your hair color.
Bonka 展示了他的最新发明：一种能够瞬间改变头发颜色的糖果。
He holds seven of these Do-Dye Drops, four red drops, two white, and one blue.
他共有七颗这种“Do-Dye Drops”彩珠：四颗红色的、两颗白色的，还有一颗蓝色的。
He then summons the magical creatures who maintain his factory, the Proofa-Boompas, to form a single-file line.
随后，他召唤出那些负责维护他工厂的魔法生物——Proofa-Boompas，让它们排成一列直线。
You’re placed at the front with four Proofa-Boompas behind you.
你被安排在队伍的最前面，身后跟着四台 Proofa-Boompa 设备。
All five of you blindly take one of the seven drops, and the leftover drops are hidden.
你们五个人中的每一个人都盲目地从那七滴液体中选择了一滴，而剩下的六滴液体则被藏了起来。
Everyone in line can see the hair transformations of those in front of them, but not their own hair or that of anyone behind them.
排队的每个人都能看到前面人的头发变化情况，却看不到自己或后面人的头发变化。
Since you are at the very front of the line, you can’t see anything.
因为你站在队伍的最前面，所以什么也看不见。
The Proofa-Boompas, who are renowned for logical reasoning, are polled from back to front, and asked, “Are you logically certain of your hair color?”
Proofa-Boompas族以出色的逻辑推理能力而闻名。他们在投票时是从后往前依次进行投票的，同时会被问到：“你对自己的头发颜色是否有十足的信心（即你是否确信自己的头发颜色是某种特定的颜色）？
You hear the following replies: no, yes, yes, yes.
你听到了以下回答：“不”、“是”、“是”、“是”。
Bonka then slyly turns to you and asks, “what is the color of your hair?”
然后，Bonka 突然转过头来，狡黠地问你：“你的头发是什么颜色的？
Pause now to figure it out for yourself.
现在先暂停一下，自己想一想这个问题吧。
Answer in 3 Answer in 2 Answer in 1
答案1：
The key to solving a logic problem like this is understanding that each Proofa-Boompa’s response
解决这类逻辑问题的关键在于明白：每个“Proofa-Boompa”的反应……（不过原句似乎不完整，此处应补充具体内容。）
depends both on the hair colors they see in front of them, and what they’ve learned from the responses behind them.
这既取决于他们眼前看到的头发颜色，也取决于他们从他人的反应中所学到的信息。
And as we go down the line, each response will help us further narrow the pool of possible hair color arrangements.
随着我们继续分析，每一个反馈都会帮助我们进一步缩小可能的发色组合范围。
We’ll start with the first Proofa-Boompa’s “no.”
我们先从 Proofa-Boompa 第一次说“不”开始讲起。
If all four hairdos in front of them were red, they still wouldn't be able to tell whether their own hair was blue or white.
即使他们面前的四种发型都是红色的，他们仍然无法分辨自己的头发是蓝色还是白色。
In fact, the only situation where they could say “yes” is if they saw two white and one blue in front of them,
事实上，他们唯一可以回答“是”的情况是，当他们看到面前有两件白色的物品和一件蓝色的物品时。
in any order.
可以按任意顺序排列。
In that case, they would know that they must be red.
在这种情况下，他们就会知道这些东西一定是红色的。
So we can eliminate that hair color combination and list out all the remaining combinations Proofa-Boompa 1 might see that would leave him uncertain.
因此，我们可以排除那种头发颜色的组合，然后列出 Proofa-Boompa 1 可能会看到的所有其他组合——这些组合都会让他感到困惑（或不确定该选择哪种颜色）。
It's important to note that for each scenario, these colors could appear in any order in positions two through five.
需要注意的是，在每种情况下，这些颜色都可能以任意顺序出现在第二到第五个位置上。
Now let’s move on to Proofa-Boompa 2, who answers “yes.”
现在我们来看看 Proofa-Boompa 2，它的回答是“是”。
We can take what we learned from Proofa-Boompa 1 and work through the remaining possibilities.
我们可以利用从 “Proofa-Boompa 1” 项目中获得的知识，来分析其余所有可能的情况。
Once again, it’s helpful to think in terms of what Proofa-Boompa 2 could see in front of them.
再一次，用“Proofa-Boompa 2”能够看到的东西来思考这个问题会很有帮助。
Say they see three red.
假设他们看到了三个红色的物体。
Based on the pool of remaining possibilities, there are scenarios in which Proofa-Boompa 2′s hair could be red,
根据现有的可能性范围来看，存在一些情况：在这种情况下，《Proofa-Boompa 2》的角色可能会拥有红色的头发。
white, or blue.
白色或蓝色。
So Proofa-Boompa 2 wouldn’t be able to say “yes” with certainty.
因此，Proofa-Boompa 2 无法确定地回答“是”或“否”。
If we keep working through cases like this, we’ll find that most leave ambiguity, and would therefore lead Proofa-Boompa 2 to say no.
如果我们继续研究这类案例，会发现大多数案例都存在模糊不清的地方，因此会导致 Proofa-Boompa 2 系统给出“拒绝”的判断。
In fact, there are only two scenarios in which the second Proofa-Boompa could be certain.
事实上，只有两种情况才能让第二个“Proofa-Boompa”系统得出确定的结论。
They see two white and one red, or they see one white, one blue, and one red.
他们可能看到两个白色的物体和一个红色的物体；也可能看到一个白色的物体、一个蓝色的物体和一个红色的物体。
In both cases, the second Proofa-Boompa could confidently conclude that their hair must be red.
在这两种情况下，第二个“Proofa-Boompa”都可以确信地得出结论：他们的头发一定是红色的。
If it were blue here, or white here, then Proofa-Boompa 1 would have said yes.
如果这里显示的是蓝色或白色，那么 Proofa-Boompa 1 就会给出“是”的回答。