The discovery of an alien monolith on planet RH-1729 has scientists across the world racing to unlock its mysteries.
在RH-1729星球发现的外星巨石碑，使全世界的科学家们竞相致力于解开它的秘密。
Your engineering team has developed an elegant probe to study it.
你的工程团队研发了一种精良的探测器来研究它。
The probe is a collection of 27 cube modules capable of running all the scientific tests necessary to analyze the monolith.
该探测器由27个立方体模块组合而成，能够运行所有分析巨石所需的科学检测。
The modules can self-assemble into a large 3x3x3 cube, with each individual module placed anywhere in the cube, and at any orientation.
这些模块可以自行组装成一个的3x3x3大立方体，其中每个独立模块可任意方向放置在立方体的任意位置。
It can also break itself apart and reassemble into any other orientation.
它还能自行解体，以任意方向重新组合。
Now comes your job. The probe will need a special protective coating for each of the extreme environments it passes through.
现在是需要你做的工作。探测器需要特殊的保护性涂层，使它能顺利通过各种极端环境。
The red coating will seal it against the cold of deep space,
红色涂层可使它密封，不受深空低温的影响，
the purple coating will protect it from the intense heat as it enters the atmosphere of RH-1729,
紫色涂层将在探测器进入RH-1729星球时，保护它免受高温影响，
and the green coating will shield it from the alien planet's electric storms.
而绿色涂层则将帮助它抵御外星球上的电子风暴。
You can apply the coatings to each of the faces of all 27 of the cubic modules in any way you like, but each face can only take a single color coating.
你可以按你喜欢的方式，给27个立方体模块的所有面都覆上涂层，但每个面只能涂一种颜色。
You need to figure out how you can apply the colors so the cubes can re-assemble themselves to show only red, then purple, then green.
你需要计算出如何涂色，才能使立体模块重新组合后，大立方体能呈现全红、然后全紫、最后全绿的模样。
How can you apply the colored coatings to the 27 cubes so the probe will be able to make the trip?
如何给27个小方块涂色，才能使探测器顺利完成这次旅程呢？
You can start by painting the outside of the complete cube red, since you'll need that regardless.
你可以先将整个立方体的外部涂成红色，因为无论如何你都需要它。
Then you can break it into 27 pieces, and look at what you have.
接着，拆成27个小块，看看它们是什么样子。
There are 8 corner cubes, which each have three red faces, 12 edge cubes, which have two red faces,
有8个角上的方块，每块都有三面涂成了红色；12个边上的方块，每块有二面是红色的；
6 face cubes, which have 1 red face, and a single center cube, which has no red faces.
6个表面的方块，只有一面红色；以及1个没有红色面的中心方块。
You've painted a total of 54 faces red at this point, so you'll need the same number of faces for the green and purple cubes, too.
此时你共计涂了54面红色，因此绿色和紫色立方体也需要相同数量的面。

When you're done, you'll have painted 54 faces red, 54 faces green, and 54 faces purple.
完成后，你将有54个面涂红色，54个面涂绿色，还有54个面涂紫色。
That's 162 faces, which is precisely how many the cubes have in total. So there's no margin for waste.
这162个面正是此立方体拥有表面数的总和。因此，也并没有浪费的余地。
If there's any way to do this, it'll probably be highly symmetrical. Maybe you can use that to help you.
如果有任何方法做到这一点，它可能是高度对称的，也许你可以利用这点。
You look at the center cube. You'd better paint it half green and half purple,
先看看中心的方块，最好涂成三面绿、三面蓝，
so you can use it as a corner for each of those cubes, and not waste a single face.
这样你可以把它作为立方体的角，同时一个面也没浪费。
There'll need to be center cubes with no green and no purple too.
还需要各有1个无绿色或者紫色的中心方块。
So you take 2 corner cubes from the red cube and paint the 3 blank faces of 1 purple, and the 3 blank faces of the other green.
所以，从红色大立方体上取2个角的小方块，然后把剩余三个面涂成紫色，再把另一块的剩余三面涂成绿色。
Now you've got the 6 face cubes that each have 1 face painted red. That leaves 5 empty faces on each.
你有6个正面方块只有一面涂红，每个留有五个空面。
You can split them in half. In the first group, you paint 3 faces green and 2 faces purple; In the second group, paint 3 faces purple and 2 green.
你可以把它们均分成两组，把第一组3个方块的三个面涂绿、两面涂紫；第二组中，则是三面紫和两面绿。
Counting on symmetry, you replicate these piles again with the colors rearranged.
基于对称性，你更换颜色并复制上述6个正面方块的规律进行涂色。
That gives you 6 with 1 green face, 6 with 1 red face, and 6 with 1 purple face.
最后得到6个一面绿色的方块、6个一面红色的方块和6个一面紫色的方块。
Counting up what you've completely painted, you see 8 corner cubes in each color,
数一数已经涂完的方块，会看到每个颜色有8个角落方块、
6 edge cubes in each color, 6 face cubes in each color, and 1 center cube.
6个边缘方块、6个表面方块和1个中心方块。
That means you just need 6 more edge cubes in green and purple.
即你只需要另外6个绿色和6个紫色的边缘方块。
And there are exactly 6 cubes left, each with 4 empty faces.
正好还剩6个方块未涂完色，每个方块有4个空面。
You paint 2 faces of each green and 2 faces of each purple.
把方块的两面涂成绿色，另两面涂成紫色。
And now you have a cube that's perfectly painted to make an incredible trip.
你会得到一个完美涂层的立方体，去完成不可思议的旅行了。
It rearranges itself to be red in deep space, purple as it enters RH-1729's atmosphere, and green when it flies through the electric storms.
它在深空中可把自己变成为红色，当进入RH-1729星球的大气层时变成紫色，飞行穿梭在电子风暴中时变成绿色。
As it reaches the monolith, you realize you've achieved something humans have dreamt of for eons: alien contact.
当它到达巨石碑时，你意识到你们实现了人类长久以来的梦想：接触外星人。