Can you solve the world’s most evil wizard riddle? - Dan Finkel

譯者: Lilian Chiu 審譯者: Tingwen Yan

The evil wizard MoldeVort has been trying to kill you for years,

邪惡巫師魔地佛多年來 處心積慮的想要把你殺掉，

and today it looks like he’s going to succeed.

今天看來他成功的機率很大。

But your friends are on their way, and if you can survive until they arrive,

但你的朋友正在趕來援救你， 如果你能撐到他們抵達，

they should be able to help stop him.

他們應該能協助你阻止他。

The evil wizard’s protective charms ward off every spell you know,

邪惡巫師的護身符咒

擋住了你知道的所有咒語，

so in an act of desperation you throw the only object in reach at him:

絕望之餘，你把手邊 唯一能拿到的東西丟向他：

Pythagoras’s cursed chessboard.

受詛咒的畢達哥拉斯棋盤。

It works, but with a catch.

這招有用，但有一個條件。

MoldeVort starts in one corner of the 5x5 board.

棋盤的大小為五乘五， 魔地佛從一個角落開始。

You have a few minutes to choose four distinct positive whole numbers.

你有幾分鐘時間可以選擇 四個不同的正整數。

MoldeVort gets to say one of them, and if you can pick a square on the board

魔地佛說出其中一個數字， 如果你在棋盤上選一個格子，

whose center is exactly that distance away,

格子中心與他的距離 剛好是那個數字，

the curse will force him to move to that spot.

詛咒就會迫使他朝向那個點前進。

Then he’ll have to choose any of the four numbers,

接著，他會再從 那四個數字中選一個，

and the process repeats until you can’t keep him inside the board

這個過程會不斷重覆，直到

遵守規則的任何移動方式 都無法讓他留在棋盤上。

with legal moves.

Then he’ll break free of the spell and almost certainly kill you.

接著他便能脫離咒語束縛， 八成就會殺了你。

What four numbers can you choose to keep MoldeVort trapped by your spell

你會選哪四個數字， 可以確保在你的支援抵達之前，

魔地佛都無法脫離你的咒語中？

long enough for help to arrive? And what’s your strategy?

你的策略是什麼？

Pause the video to figure it out yourself.

〔在此暫停作答〕

Answer in 3

答案即將公佈：三

Answer in 2

答案即將公佈：二

Answer in 1

答案即將公佈：一

The trick here is to keep MoldeVort where you want him.

這裡要用的技巧是要讓魔地佛 留在你希望的位置。

And one way to figure out how to do that

至於要怎麼做到，其中一個方法

is to play out the game as MoldeVort would:

是模仿魔地佛的方式來進行比賽：

always trying to escape.

不斷嘗試逃脫。

You’re dealing with a relatively small board,

相對之下，這個棋盤比較小，

so the numbers can’t be too big.

所以數字不能太大。

Let’s start by trying 1, 2, 3, 4 to see what happens.

咱們一開始先嘗試一、二、 三、四，看看會發生什麼事。

Moldevort could escape those numbers in just three moves.

魔地佛只要移動三次 就可以逃脫這個棋盤。

By saying 2, then 3,

他可以先說二，再說三，

he would force you to let him into one of the middle points of the grid,

就會迫使你讓他進入 其中一個中央的格子，

and then a 4 would break him free.

接著，只要說四，他便能脫身。

But that means you’ll need to allow a number larger than 4,

但，那就表示你得要選 一個比四還大的數字，

which is the distance from one end of a row to another.

而從棋盤一端 到另一端的距離就是四。

How is that even possible?

這樣怎麼可能成功？

Through diagonal moves.

透過對角線移動。

There are, in fact, points that are distance 5 from each other,

事實上，有些格子 之間的距離是五，

which we know thanks to the Pythagorean Theorem.

這點是畢氏定理告訴我們的。

That states that the squares of the sides of a right triangle

畢氏定理指出， 正三角形兩邊的平方

add up to the square of its hypotenuse.

加起來會等於斜邊的平方。

One of the most famous Pythagorean triples is 3, 4, 5,

畢氏定理最著名的例子是 邊長為三、四、五的三角形，

and that triangle is hiding all over your chessboard.

而你的棋盤上滿是這種三角形。

So if MoldeVort was here, and he said 5, you could move him to these spaces.

如果魔地佛在這裡，當他說五，

你便可以把他移到這些位置。

There’s another insight that will help.

還有另一項有幫助的洞見。

The board is very symmetrical: If MoldeVort is in a corner,

棋盤非常對稱：如果 魔地佛在其中一個角落，

it doesn’t really matter to you which corner it is.

對你來說，是哪個角落都無所謂。

So we can think of the corners as being functionally the same,

就功能面來說， 所有的角落是相同的，

and color them all blue.

將它們標記為藍色。

Similarly, the spaces neighboring the corners behave the same as each other,

同樣的，在角落旁邊的格子， 也都有相同的行為，

and we’ll make them red.

把它們標記為紅色。

Finally, the midpoints of the sides are a third type.

最後，每邊中央的格子 是屬於第三類。

So instead of having to develop a strategy

所以，我們不用 為棋盤邊緣的十六個格子

for each of the 16 spaces on the outside of the board,

設計十六種策略，

we can reduce the problem to just three.

問題可以簡化為 只要設計三種策略。

Meanwhile, all the inside spaces are bad for us,

同時，中央區的格子 對我們而言都是不利的，

because if MoldeVort ever reaches one,

因為只要魔地佛能 到其中任何一格，

he’ll be able to say any number larger than 3 and go free.

再說出比三更大的數字， 就能成功脫身。

Orange spaces are trouble too, since any number except 1, 2, or 4

橘色的格子也很麻煩，

因為任何一個不是 一、二、四的數字

would take him to an inside space or off the board.

就能讓他進入棋盤的 中央區域或是脫離棋盤。

So orange is out and you’ll need to keep him on blue and red.

所以橘色也不能用，你要讓他 留在藍色和紅色的格子裡。

That means 2 is bad,

那就表示二不適合，

since it could take MoldeVort to orange on the first turn.

因為二會讓魔地佛在第一輪 就進入橘色格子。

But the four other smallest numbers, 1, 3, 4, and 5, might work.

但其他四個最小的數字，

即一、三、四、五，可能行得通。

Let’s try them and see what happens.

咱們來試試，看結果會如何。

If MoldeVort says 1, you can make him go from blue to red or red to blue.

如果魔地佛說一，

你可以讓他從藍色移到紅色， 或從紅色移到藍色。

And the same works if he says 3.

如果他選擇三，也是如此。

Thanks to our diagonals, this is even true if he says 5.

好在有對角線，即使他 選擇五，這招還是行得通。

If he says 4, you can keep him on the color he’s already on

如果他選擇四，你可以 讓他直向或橫向移動，

by moving the length of a row or column.

進入一個和目前同樣顏色的格子，

So these four numbers work!

所以這四個數字是可行的！

Even if your friends don’t get here right away,

即使你的朋友無法馬上趕到，

you’ll be able to keep the world’s most evil wizard

你也能困住世界上最邪惡的巫師，

contained for as long as you need.

且要把他困住多久都行。