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The evil wizard MoldeVort has been trying to kill you for years, and today it looks like he's going to succeed.
邪恶的巫师莫地魔多年来处心积虑要把你杀掉，看来今天他就要成功了。
But your friends are on their way, and if you can survive until they arrive, they should be able to help stop him.
但是你的朋友正在赶来的路上，如果你能坚持到他们赶到，他们可以帮你阻止他。
The evil wizard's protective charms ward off every spell you know, so in an act of desperation you throw the only object in reach at him: Pythagoras's cursed chessboard.
邪恶巫师的护身符咒抵挡了你知道的所有魔咒，因而在绝望之余，你把手边唯一能够到的东西扔向他：受诅咒的毕达哥拉斯棋盘。
It works, but with a catch. MoldeVort starts in one corner of the 5x5 board.
这招有用，但却内藏玄机。棋盘大小为5x5，莫地魔从一个角落开始。
You have a few minutes to choose four distinct positive whole numbers.
你有几分钟去选择四个不同的正整数。
MoldeVort gets to say one of them, and if you can pick a square on the board whose center is exactly that distance away, the curse will force him to move to that spot.
莫地魔说出其中一个数字，如果你能在棋盘上选一个格子，格子中心与他的距离刚好是那个数字，诅咒将迫使他移动到你选的格子。
Then he'll have to choose any of the four numbers, and the process repeats until you can't keep him inside the board with legal moves.
之后，他会再从四个数字中选择任意一个，这个步骤会不断重复，直到按规则的任意移动都无法让他留在棋盘内。
Then he'll break free of the spell and almost certainly kill you.
然后，他便能摆脱诅咒束缚，几乎肯定他会杀了你。
What four numbers can you choose to keep MoldeVort trapped by your spell long enough for help to arrive? And what's your strategy?
你要选择哪四个数字可以确保在支援抵达前莫地魔都无法摆脱你的咒语？那么，你的策略是什么？
The trick here is to keep MoldeVort where you want him. And one way to figure out how to do that is to play out the game as MoldeVort would: always trying to escape.
这里的诀窍是要让莫地魔留在你希望的地方。其中一个可以做到的方法是用莫地魔的思维玩这个游戏：不断尝试逃脱。
You're dealing with a relatively small board, so the numbers can't be too big. Let's start by trying 1, 2, 3, 4 to see what happens.
这个棋盘相对较小，所以数字不能太大。让我们先尝试1、2、3、4，看看会发生什么。
Moldevort could escape those numbers in just three moves.
莫地魔只需用三步就能逃出来。
By saying 2, then 3, he would force you to let him into one of the middle points of the grid, and then a 4 would break him free.
他可以说2，然后再说3，就会迫使你让他移动到棋盘的中心一个格子，接着，他只需说4，就可以逃出来了。
But that means you'll need to allow a number larger than 4, which is the distance from one end of a row to another. How is that even possible?
但这意味着你要选择一个大于4的数字，而从棋盘一端到另一端的距离就是4格。这怎么可能成功呢？
Through diagonal moves. There are, in fact, points that are distance 5 from each other, which we know thanks to the Pythagorean Theorem.
通过对角移动。实际上，这里有方块相隔5步，这点要多亏勾股定理。
That states that the squares of the sides of a right triangle add up to the square of its hypotenuse.
勾股定理指出，三角形的两条边的平方相加等于最长边的平方。
One of the most famous Pythagorean triples is 3, 4, 5, and that triangle is hiding all over your chessboard.
勾股定理最著名的例子就是边长为3、4、5的三角形，而你的棋盘上满是这些三角形。
So if MoldeVort was here, and he said 5, you could move him to these spaces. There's another insight that will help.
所以如果莫地魔在这里，说了5，你可以让他挪到这些位置。还有另一项有帮助的想法。
The board is very symmetrical: If MoldeVort is in a corner, it doesn't really matter to you which corner it is.
这个棋盘非常对称：如果莫地魔在其中一个角落，对你而言，他在哪个角落并不重要。
So we can think of the corners as being functionally the same, and color them all blue.
就功能而言，我们可以想所有角落是相同的，将它们标记为蓝色。
Similarly, the spaces neighboring the corners behave the same as each other, and we'll make them red.
同样地，邻近角落的方块也是一样的，我们把它们标记为红色。
Finally, the midpoints of the sides are a third type.
最后，每条边的中央格子是属于第三类。
So instead of having to develop a strategy for each of the 16 spaces on the outside of the board, we can reduce the problem to just three.
所以，我们不用为棋盘边缘的16个格子全都设计策略，我们可以简化问题至三种思路。
Meanwhile, all the inside spaces are bad for us, because if MoldeVort ever reaches one, he'll be able to say any number larger than 3 and go free.
同时，中间区域格子都对我们不利，因为只要莫地魔来到了其中之一，他就可以说一个大于3的数字获得自由。
Orange spaces are trouble too, since any number except 1, 2, or 4 would take him to an inside space or off the board.
橙色的地方也有麻烦，因为数字除了1、2、4都会让他脱身或来到中间区域。
So orange is out and you'll need to keep him on blue and red. That means 2 is bad, since it could take MoldeVort to orange on the first turn.
所以不能选择橙色，你需要把他留在蓝色和红色内。这意味着2是不合适的，因为这会让莫地魔第一局就来到橙色地带。
But the four other smallest numbers, 1, 3, 4, and 5, might work. Let's try them and see what happens.
但是其他的四个最小的数字1、3、4、5则可行。让我们尝试一下会发生什么。
If MoldeVort says 1, you can make him go from blue to red or red to blue. And the same works if he says 3.
如果莫地魔说1，你可以让他去蓝到红或者红到蓝。如果他选择3也是一样的。
Thanks to our diagonals, this is even true if he says 5.
多亏我们的对角线，所以5也行得通。
If he says 4, you can keep him on the color he's already on by moving the length of a row or column. So these four numbers work!
如果他说了4，你可以让他直向或者横向移动。所以这四个数字行得通！
Even if your friends don't get here right away, you'll be able to keep the world's most evil wizard contained for as long as you need.
就算你的朋友不能立刻赶到，你也能困住世界上最邪恶的巫师，让他在棋盘上困多久都行。
