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你能解开外星探测器谜题吗?

Can you solve the alien probe riddle? - Dan Finkel

此集末尾有个附送谜题 不要走开噢
Stick around after this episode for a bonus riddle.
在RH-1729行星上发现了一个外星巨石
The discovery of an alien monolithon planet RH-1729
这一发现一时间让全世界的科学家争先恐后地想要解开谜团
has scientists across the worldracing to unlock its mysteries.
你的工程团队已经研发出了一个设计优良的探测器准备展开研究
Your engineering team has developedan elegant probe to study it.
这个探测器是由27个立方体模块组成的
The probe is a collectionof 27 cube modules
并可以运行所有对于分析庞然大物所必需的科学试验
capable of running all the scientific tests necessary to analyze the monolith.
这些模块可以自行组装成一个大型3x3x3的立方体
The modules can self-assembleinto a large 3x3x3 cube,
而每个独立的模块可以位于立方体的任意位置
with each individual moduleplaced anywhere in the cube,
任何方向
and at any orientation.
这一立方体也可以自行解体并朝任意方向再次组装
It can also break itself apart and reassemble into any other orientation.
现在轮到你工作了
Now comes your job.
这一探测仪需要特殊的保护涂层
The probe will need a specialprotective coating
这是为了应对它所经过的极端环境
for each of the extremeenvironments it passes through.
红色涂层能抵御外太空的寒冷
The red coating will seal it against the cold of deep space,
当它进入RH-1729的大气层
the purple coating will protect itfrom the intense heat
紫色涂层能抵御高温
as it enters the atmosphere of RH-1729,
而绿色涂层能防御
and the green coating will shield it
外星的电暴
from the alien planet’s electric storms.
你可以给27个立方体模块的
You can apply the coatings to each of the faces
每一个面都涂上涂层
of all 27 of the cubic modules
以任何你喜欢的方式
in any way you like,
但每一面只能涂一种颜色的涂层
but each face can only take a single color coating.
你得想想怎么涂色
You need to figure out how youcan apply the colors
才能使立方体重新组合成只有红色
so the cubes can re-assemble themselvesto show only red,
接着只有紫色 然后只有绿色
then purple, then green.
你该怎样给这27个立方体涂色
How can you apply the colored coatingsto the 27 cubes
才能使探测仪顺利地完成探测?
so the probe will be ableto make the trip?
如果你想自己找出解决方法 就在此处暂停一下
Pause here if you wantto figure it out yourself.
你可以从给表层全部涂上红色开始
You can start by painting the outside of the complete cube red,
因为无论如何你都需要达到这一步
since you’ll need that regardless.
然后 你可以把它分成27块
Then you can break it into 27 pieces,
看看现在你有什么
and look at what you have.
你有8个位于顶角且有三面是红色的立方块
There are 8 corner cubes,which each have three red faces,
12个位于棱上且有两面是红色的立方块
12 edge cubes,which have two red faces,
6个位于表面 且有一面是红色的立方体
6 face cubes, which have 1 red face,
还有1个位于中心 且没有被涂红的立方体
and a single center cube,which has no red faces.
目前你一共给54个面涂了红色
You’ve painted a total of 54 faces red at this point,
所以你需要同等数量的
so you’ll need the same number of faces
绿面和紫面的立方体
for the green and purple cubes, too.
当你完成后 你会得到涂好的54个红面
When you’re done,you’ll have painted 54 faces red,
54个绿面和54个紫面
54 faces green, and 54 faces purple.
也就是162个面
That’s 162 faces,
刚好是立方块面的数量的总和
which is precisely how many the cubes have in total.
所以没有浪费的余地
So there’s no margin for waste.
如果存在任何可行的办法
If there’s any way to do this,
那它很可能是高度对称的
it’ll probably be highly symmetrical.
也许你可以利用这条规律解决问题
Maybe you can use that to help you.
看看位于中心的立方块体
You look at the center cube.
你最好把它涂成一半绿一半紫
You’d better paint it half greenand half purple,
这样就可以把它用作那些立方体的顶角
so you can use it as a corner for each of those cubes,
连一面都不会浪费
and not waste a single face.
现在仍然需要位于中心
There’ll need to be center cubes
且没有绿面和紫面的立方体
with no green and no purple too.
所以从红色立方块中取两个位于顶角的立方块
So you take 2 corner cubesfrom the red cube
然后把其中一个立方块的空白三面涂紫
and paint the 3 blank faces of 1 purple,
把另一个的立方块的空白三面涂绿
and the 3 blank faces of the other green.
现在你有六个位于表面
Now you’ve got the 6 face cubes
且每个都有一面是红色的立方块
that each have 1 face painted red.
于是每个立方块都有五个空白面
That leaves 5 empty faces on each.
你可以把它们分成两组
You can split them in half.
把第一组中的立方块涂成三面绿 两面紫
In the first group,you paint 3 faces green and 2 faces purple;
把第二组中的立方块涂成三面紫 两面绿
In the second group, paint 3 faces purple and 2 green.
靠对称性
Counting on symmetry,
通过对颜色的重新排列重复这些操作
you replicate these piles again with the colors rearranged.
你得到了6个有一绿面
That gives you 6 with 1 green face,
6个有一红面 6个有一紫面的立方块
6 with 1 red face, and 6 with 1 purple face.
把所有被涂满的立方块加起来
Counting up what you’ve completely painted,
得到了每种颜色都有8个位于顶角的
you see 8 corner cubes in each color,
6个位于棱上的
6 edge cubes in each color,
6个位于表面的立方块
6 face cubes in each color,
和1个位于中心的立方块
and 1 center cube.
这意味着再需要6个涂绿和涂紫的立方块
That means you just need 6 more edge cubes in green and purple.
而且刚好剩下6个立方块 每个立方块都有四个空白面
And there are exactly 6 cubes left, each with 4 empty faces.
给每个立方块涂上两面绿色和两面紫色
You paint 2 faces of each green and 2 faces of each purple.
现在你有了一个上色完美的立方体
And now you have a cube that ’
可以完成一个奇妙之旅
s perfectly painted to make an incredible trip.
在太空深处 它可自行重组成纯红色
It rearranges itselfto be red in deep space,
当进入RH-1729的大气层时 成纯紫色
purple as it enters RH-1729’s atmosphere,
当穿越电暴时 成纯绿色的立方体
and green when it flies throughthe electric storms.
当它到达庞然大物之时
As it reaches the monolith,
你发现你已实现人类长久以来的梦想:
you realize you’ve achieved something humans have dreamt of for eons:
与外星人接触
alien contact.
这是给立方体上色的一种方法 但不是唯一的一种
That’s one method to paint the cubes but it’s not the only one
今日的附送谜题是这个
Today’s bonus riddle is this.
有多少种不同的方法给这些立方块上色?
How many distinct ways are there to paint the cubes?
也就是说 不同的方法中27个小立方块中的一部分是不相同的
In other words, some of the 27 smaller cubes will be different from method to method.
但是它们每次组合起来仍然是红色
They can still be assembled into red,
紫色和绿色的3x3x3立方体
purple and green 3x3x3 cubes everytime.
如果你不确定怎么开始
If you’re not sure how to get started,
点击下方描述栏中的链接进入BRILLIANT
head on over to BRILLIANT by using the link in the description below.
我们在BRILLIANT的伙伴已经做出了出色的探索
Our partners at BRILLIANT have created an excellent exploration
它会引导你解决问题 而不是直接给出答案
that will guide you towards the solution without just giving away the answer.
你会学习如何把问题拆分成几部分
You’ll learn how to break the problem into its component pieces,
透彻地思考每个部分并整合重构 最终得出结论
think clearly through each part and build it backup to a conclusion.
进入网站后 可以考虑注册一个高级帐户
And while you’re there, consider signing up for a premier account
前833个注册高级帐户的用户能获得八折的年度订阅优惠
First 833 of you to do so will get 20% off the annual subscription.

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视频概述

如何涂色才能使探测器完成使命

听录译者

收集自网络

翻译译者

infinite

审核员

审核员@XG

视频来源

https://www.youtube.com/watch?v=SXXrQlJoNsw

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