你可以解开世界上最邪恶巫师的谜题吗?- 丹 · 芬克 Dan Finkel: Can you solve the world's most evil wizard riddle?

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演员: Dan Finkel

The evil wizard MoldeVort has been trying to kill you for years,
邪恶的巫师莫地魔 多年来处心积虑要把你杀掉,
and today it looks like he’s going to succeed.
But your friends are on their way, and if you can survive until they arrive,
但是你的朋友正在赶来的路上, 如果你能坚持到他们赶到,
they should be able to help stop him.
The evil wizard’s protective charms ward off every spell you know,
邪恶巫师的护身符咒 抵挡了你知道的所有魔咒,
so in an act of desperation you throw the only object in reach at him:
因而在绝望之余,你把手边 唯一能够到的东西扔向他:
Pythagoras’s cursed chessboard.
It works, but with a catch.
MoldeVort starts in one corner of the 5x5 board.
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.
MoldeVort gets to say one of them, and if you can pick a square on the board
莫地魔说出其中一个数字, 如果你能在棋盘上选一个格子,
whose center is exactly that distance away,
the curse will force him to move to that spot.
Then he’ll have to choose any of the four numbers,
之后,他会再从四个数字中 选择任意一个,
and the process repeats until you can’t keep him inside the board
这个步骤会不断重复, 直到按规则的任意移动
with legal moves.
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
你要选择哪四个数字 可以确保在支援抵达前
long enough for help to arrive? And what’s your strategy?
莫地魔都无法摆脱你的咒语? 那么,你的策略是什么?
Pause the video to figure it out yourself.
Answer in 3
3 秒后公布答案
Answer in 2
2 秒后公布答案
Answer in 1
1 秒后公布答案
The trick here is to keep MoldeVort where you want him.
这里的诀窍是要让莫地魔 留在你希望的地方。
And one way to figure out how to do that
is to play out the game as MoldeVort would:
always trying to escape.
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.
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.
By saying 2, then 3,
他可以说 2 ,然后再说 3 ,
he would force you to let him into one of the middle points of the grid,
就会迫使你让他移动到 棋盘的中心一个格子,
and then a 4 would break him free.
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,
但这意味着你要选择 一个大于 4 的数字,
which is the distance from one end of a row to another.
而从棋盘一端到 另一端的距离就是 4 格。
How is that even possible?
Through diagonal moves.
There are, in fact, points that are distance 5 from each other,
实际上,这里有方块相隔 5 步,
which we know thanks to the Pythagorean Theorem.
That states that the squares of the sides of a right triangle
勾股定理指出, 三角形的两条边的平方相加
add up to the square of its hypotenuse.
One of the most famous Pythagorean triples is 3, 4, 5,
勾股定理最著名的例子 就是边长为 3、4、5 的三角形,
and that triangle is hiding all over your chessboard.
So if MoldeVort was here, and he said 5, you could move him to these spaces.
所以如果莫地魔在这里,说了 5 , 你可以让他挪到这些位置。
There’s another insight that will help.
The board is very symmetrical: If MoldeVort is in a corner,
这个棋盘非常对称: 如果莫地魔在其中一个角落,
it doesn’t really matter to you which corner it is.
So we can think of the corners as being functionally the same,
就功能而言,我们可以想 所有角落是相同的,
and color them all blue.
Similarly, the spaces neighboring the corners behave the same as each other,
and we’ll make them red.
Finally, the midpoints of the sides are a third type.
So instead of having to develop a strategy
for each of the 16 spaces on the outside of the board,
16 个格子全都设计策略,
we can reduce the problem to just three.
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.
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
橙色的地方也有麻烦, 因为数字除了 1、2、4
would take him to an inside space or off the board.
So orange is out and you’ll need to keep him on blue and red.
所以不能选择橙色, 你需要把他留在蓝色和红色内。
That means 2 is bad,
这意味着 2 是不合适的,
since it could take MoldeVort to orange on the first turn.
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.
但是其他的四个最小的数字 1、3、4、5 则可行。
Let’s try them and see what happens.
If MoldeVort says 1, you can make him go from blue to red or red to blue.
如果莫地魔说 1, 你可以让他去蓝到红或者红到蓝。
And the same works if he says 3.
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
如果他说了 4 , 你可以让他直向
by moving the length of a row or column.
So these four numbers work!
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.