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Once each year, thousands of logicians descend into the desert for Learning Man,
每年一度，成千上万的逻辑学家在沙漠中参加“学习者”活动，
a week-long event they attend to share their ideas, think through tough problems... and mostly to party.
一个为期一周的活动，参加以分享他们的想法，思考棘手的问题...以及主要为了聚会。
And at the center of that gathering is the world's most exclusive club, where under the full moon, the annual logician's rave takes place.
而这个聚会的中心是世界上最独特的俱乐部，满月的时候，一年一度的逻辑学家狂欢在这里举行。
The entry is guarded by the Demon of Reason, and the only way to get in is to solve one of his dastardly challenges.
入口由“理性之魔”把守，进入的唯一方法是解决他的一个卑鄙的挑战。
You're attending with 23 of your closest logician friends, but you got lost on the way to the rave and arrived late.
你和你最亲密的23位逻辑学家朋友一起参加，但你在去的路上迷路而迟到了。
They're already inside, so you must face down the demon alone.
他们已经在里面了，所以你必须独自面对这个恶魔。
He poses you the following question: When your friends arrived, the demon put masks on their faces and forbade them from communicating in any way.
他向你提出了如下问题：当你的朋友到达时，恶魔给他们的脸上都戴了面具并禁止他们以任何方式进行交流。
No one at any point could see their own masks, but they stood in a circle where they could see everyone else's.
没有人在任何时候可以看到自己的面具，但他们站成一个圈子，可以看到所有其他人的面具。
The demon told the logicians that he distributed the masks in such a way that each person would eventually be able to figure out their mask's color using logic alone.
恶魔告诉逻辑学家们，以他分配面具的方式，每个人最终都能找出自己面具的颜色，且只使用逻辑。
Then, once every two minutes, he rang a bell. At that point, anyone who could come to him and tell him the color of their mask would be admitted.
然后，每隔两分钟，他按一下铃。到时候，任何能来找他并告诉恶魔自己面具颜色的人都会被接纳。
Here's what happened: Four logicians got in at the first bell. Some number of logicians, all in red masks, got in at the second bell.
这是发生的情况：四位逻辑学家在第一次铃响时就进了场。一些都戴着红色面具的逻辑学家，在第二次铃响时进入了。
Nobody got in when the third bell rang. Logicians wearing at least two different colors got in at the fourth bell.
第三次铃响时，无人进入。至少两种不同颜色面具的逻辑学家们在第四次铃响时进入了。
All 23 of your friends played the game perfectly logically and eventually got inside.
你所有的23位朋友都完全符合逻辑地进行了游戏，并最终进入了里面。
Your challenge, the demon explains, is to tell him how many people gained entry when the fifth bell rang. Can you get into the rave?
你的挑战，恶魔解释道，是要告诉他第五次铃响时有多少人进入。你能进入狂欢吗？
It's initially difficult to imagine how anyone could, using just logic and the colors they see on the other masks, deduce their own mask color.
起初很难想象任何人能够仅凭逻辑和他们在别人面具上看到的颜色，推断出自己的面具颜色。
But even before the first bell, everyone will realize something critical.
但在第一次铃响前，每个人就会意识到一些关键的问题。
Let's imagine a single logician with a silver mask. When she looks around, she'd see multiple colors, but no silver.
让我们想象一下，一个独自戴着银色面具的逻辑学家。当她环顾四周时，她会看到多种颜色，但没有银色。
So she couldn't ever know that silver is an option, making it impossible for her to logically deduce that she must be silver.
所以她永远不可能知道银色是一个选项，使她不可能在逻辑上推断出她一定是银色的。
That contradicts rule five, so there must be at least two masks of each color.
这与第五条规则冲突，所以每种颜色至少有两个面具。
Now, let's think about what happens when there are exactly two people wearing the same color mask. Each of them sees only one mask of that color.
现在，让我们思考一下当两个人戴着同一颜色的面具时会发生什么。他们每人只能看到该颜色的一个面具。
But because they already know that it can't be the only one, they immediately know that their own mask is the other.
但因为他们已经知道该颜色的面具不可能是唯一，他们会立即知道，自己的面具就是另一个。
This must be what happened before the first bell: two pairs of logicians each realized their own mask colors when they saw a unique color in the room.
这一定发生在第一次铃响前：两对逻辑学家各自意识到了他们自己的面具颜色，当他们在场上看到一种独特的颜色时。
What happens if there are three people wearing the same color?
那如果是三个人戴着相同颜色的面具呢？
Each of them -- A, B and C -- sees two people with that color.
他们中的每个人，A、B和C，都看到了该颜色面具的两个人。
From A's perspective, B and C would be expected to behave the same way that the orange and purple pairs did, leaving at the first bell.
从A的角度来看，B和C会预计做出同样的行为，如橙色和紫色的两对一样，在第一次铃响时离开。
When that doesn't happen, each of the three realizes that they are the third person with that color, and all three leave at the next bell.
当该情况没有发生时，三人都会各自意识到他们是第三个有该颜色的人，然后三人都会在下次铃响时离开。
That was what the people with red masks did -- so there must have been three of them.
这就是那些戴着红色面具的人做的--所以他们肯定有三个人。
We've now established a basis for inductive reasoning.
我们现在已经建立了一个归纳推理的基础。
Induction is where we can solve the simplest case, then find a pattern that will allow the same reasoning to apply to successively larger sets.
归纳法是我们可以解决最简单的情况，然后找到一个模式进行同样的推理以适用于接下来的更大集合。
The pattern here is that everyone will know what group they're in as soon as the previously sized group has the opportunity to leave.
这里的模式是每个人都会知道自己在哪个组中，一旦前一个规模的组别有机会离开。
After the second bell, there were 16 people. No one left on the third bell, so everyone then knew there weren't any groups of four.
第二次铃响过后，剩16人。第三次铃响时无人离开，所以大家都会知道没有任何四人的组别。
Multiple groups, which must have been of five, left on the fourth bell.
几个组别，一定是五人的，在第四次铃响时离开。
Three groups would leave a solitary mask wearer, which isn't possible, so it must've been two groups.
若是三组五个人，将留下单独戴面具的一人，这是不可能的，所以一定是两组。
And that leaves six logicians outside when the fifth bell rings: the answer to the demon's riddle.
那么在第五次铃响时，会剩下六位逻辑学家：这便是恶魔谜题的答案。
Nothing left to do but join your friends and dance.
没有其他要做的了，加入你的朋友跳舞吧。
