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It's your first day in your new job as Center Realm's official cartographer, and you've already got a big problem.
这是你作为中央王国官方制图师的第一天，你已经遇上了一个大问题。
Center Realm is home to three elder dragons: two ice, one fire, and they've lived in harmony on the east coast for centuries.
中央王国是三条远古龙的家：两条冰龙，一条火龙，他们已经在东海岸和睦地生活了几个世纪。
But scouts have sighted three fire dragons and five ice dragons flying across the Western Ocean.
但是侦察兵们看到三条火龙和五条冰龙正在飞越西部海洋。
You'll only have a few hours to assign them their designated regions before they'll arrive.
在他们到达之前，你只有几个小时的时间给他们分配指定的地区。
Elder dragons are extremely territorial. Each must have its own, officially acknowledged stomping ground.
远古龙的领地意识非常强。每一条都必须有自己的、得到官方承认的领地。
They'll peacefully roost there unless their region borders another dragon of the same type, in which case the matching dragons will go on a rampage.
他们将和平地栖息在那里，除非他们的领地与另一条同类的龙的领地接壤在这种情况下，这对龙会大打出手。
However, fire and ice dragons can border each other, and matching regions can touch at corners.
然而，火龙和冰龙的领地可以相互接壤，同种领域之间也允许角落相接。
You'll soon have 11 dragons and just 8 regions.
你很快就会迎来11条龙和有限的8个地区。
Fortunately, you have enough political capital to create 3 new regions, each of which must be completely enclosed spaces.
幸运的是，你有足够的政治资本来建立三个新的地区，每一个都必须是完全封闭的。
Add more or otherwise mess this up, and you'll lose your job and your head. Where do you draw lines and place the new dragons?
继续增加，或者用其它方式把事情搞砸，你就会丢掉工作和脑袋。你将在哪里画线来安置新来的龙？
It isn't difficult to create three new regions.
建立三个新的区域并不困难。
What is more challenging is to make sure the result will keep each dragon away from its own kind.
更具挑战性的是确保每条龙都远离自己的同类。
For instance, this can be neither ice nor fire, because it borders both.
比如，这个区域不可以是冰也不能是火，因为它与两者都接壤。
However, create a new region like this, and suddenly there are viable options.
然而，创建一个像这样的新区域，就瞬间提供了可行的选择。
Why did that work? Look at the point where these four regions meet.
这样为什么可行呢？看看这四个区域的交汇点。
If you go around it, it alternates between fire and ice. Before the new line was added, that wouldn't have worked.
如果你绕过了它，就会在火和冰之间交替。在增加新线之前，这是行不通的。
Nor would 5 or 7 regions. 6 and 8, however, both do.
分成5个或7个区域也不行。但是分成6个或8个，便都可以。
The pattern is that points where lines meet must be surrounded by an even number of regions.
这其中的模式是线相交的点必须被偶数的区域包围。
As long as that's true, you can color the map in two colors, by alternating them around those points.
只要这一点成立，你就可以只用两种颜色给地图上色，方法是围绕这些点交替使用。
In our initial arrangement, there were six such meeting points. So what we want to do is connect those to each other.
在我们最初的筹备中，有六个这样的交汇点。所以我们要做的就是把它们连接起来。
Each line adds a single new region that touches both meeting points. There are several ways to do this to accommodate all 8 new dragons.
每条线都增加一个新的区域，该区域与两个交汇点相接触。有几种方法都可以做到，容纳下8条新龙。
You've done such a great job that your boss puts you in a ship and sends you out across the Western Sea to investigate where these new dragons are coming from.
你做得实在太好了，你的老板把你送上了一条船，并派你穿越西海去调查这些新龙是从哪里来的。
There you're met with a civilization in disarray.
在那里你会遇到一个混乱的文明。
Their 17 elder dragons are ravaging the countryside, wiping out the peasants, devastating all the people and their thatch-roofed cottages.
他们的17条古龙正在肆虐农村，屠杀农民，毁灭了所有的人和他们的茅草屋。
And here there aren't just ice and fire dragons, but lightning dragons too. Their people will only allow the creation of two new regions.
这里不仅有冰龙和火龙，还有闪电龙。他们的人民只允许创建两个新的地区。
Where do you create new regions and place all the dragons?
你将在哪里建立新的区域并安置所有的龙？
Unfortunately, our meeting-point trick won't suffice now that there are three dragon types, so we need to find another method to identify problem areas.
不幸的是，我们的交汇点技巧对此无能为力因为现在有三种龙，所以我们需要找到另一种方法，来识别问题区域。
A great way to do so is to experiment: focus on one area and start coloring until we run out of possibilities.
一个好方法是进行实验：专注于一个地方，然后开始着色，直到穷尽所有可能性。
Take this section. These 3 regions all border each other, so they need to be different colors.
以这一部分为例。这三个区域相互接壤，所以它们需要不同的颜色。
But they also all touch this giant territory, which we now can't color.
但是他们也都接触到了这个我们现在无法上色的巨大领地。
To generalize the issue, when there are 4 regions that all border each other, it's impossible to color them with three colors.
概括地说就是，当有4个地区彼此接壤时，只用三种颜色是不可能的。
The map has two other such areas. So what you need to do is break them up.
地图上还有另外两个这样的区域。所以你需要做的就是拆散它们。
And once again, the key is drawing lines between points where multiple problematic regions touch.
同样，关键是在多个问题区域接触的点之间画线。
No matter how you do it, you'll effectively subdivide the giant territory into smaller ones. Now coloring the map becomes a logic puzzle.
不管你是怎么做的，你都能把这片巨大的领地，有效地细分成更小的领地。现在给地图着色变成了一个逻辑难题。
So long as you approach it systematically by starting in one area and radiating out,
只要你系统地从一个区域开始，向外辐射，
you'll reach an arrangement that you can fit all your dragons into, shifting the colors as needed.
你就可以完成一种安排，把所有的龙都安置好，根据需要改变颜色。
Just assign this region last, because it'll have two options. You've saved not one, but two continents from certain ruin.
最后分配这个区域，因为它有两种选择。你拯救了不只一个，而是两个大陆免于毁灭。
Now to see if you can find a giant eagle and hitch a ride back home.
现在看看你是否能找到一只巨鹰，让它载你回家吧。
