Can you solve the trickster god riddle? - Alex Rosenthal

譯者: Lilian Chiu 審譯者: SF Huang

Ragnarok has been raging for far too long;

諸神黃昏之役，實在持續太久了；

已經有許多神和英雄陣亡，

many gods and heroes have fallen, and the rest can barely stand.

剩下的也無力再戰。

Loki, his bright eyes dimmed by exhaustion,

洛基眼中閃爍的光芒 已經被疲憊給蓋過，

asks to meet.

他要求會面。

He proposes that you and he settle the conflict with a game

他提議你和他用一場遊戲 來解決這場衝突，

atop a sacred table engraved with your names.

比賽會在一張刻有 你們名字的聖桌上進行。

It has the following rules:

規則如下：

one player will carve any number of crosses into the table,

由一名玩家在桌上刻下「Ｘ」， 要刻幾個都可以，

then play begins.

接著遊戲就開始。

Each turn, the active player must carve a line

每回合，輪到的玩家 就必須要刻下一條連線，

connecting two open ends without touching itself or another line.

連接兩個開放端，且這條線 不能與自身或其他線相交。

Then, he must carve a short segment across that new line

接著，他必須在這條 新的線上面再刻一條短線段，

and pass the knife to the other player.

並把刀子交給另一位玩家。

Only crosses and end-of-turn segments are in play.

在遊戲中只能連結Ｘ 及每回合結束時刻下的短線段。

Whoever makes the last valid move wins and will rule the new world.

刻下最後一條有效連線的玩家 就是贏家，將能統治新世界。

Loki will let you carve however many crosses you want into the table,

洛基會讓你在桌上刻下Ｘ， 要刻幾個都可以，

then he’ll choose whether he goes first or second.

接著他會決定由他先開始 還是由你先開始。

You’re certain the trickster is up to something,

你很肯定這個惡作劇高手 一定有什麼盤算，

so how can you beat him?

你要如何打敗他？

Pause here to figure it out yourself. Answer in 3

若要自行解題，在此暫停。 答案即將公佈：3

Answer in 2

答案即將公佈：2

Answer in 1

答案即將公佈：1

Often the best way to analyze a game like this—

要分析這類遊戲，最好的方法——

which was invented by John Conway under the name Brussels Sprouts—

此遊戲是由約翰 ‧ 康威發明， 原名叫做布魯塞爾芽——

is to try it out.

就是用試的。

Let’s start with the simplest case: a single cross.

讓我們從最簡單的情況 開始：只有一個Ｘ。

Here, no matter how we play, the game ends in three moves.

不論我們怎麼玩， 遊戲都會在三步時結束。

With two crosses, the game always ends in eight.

若有兩個Ｘ，遊戲一定 會在八步時結束。

And with three crosses, 13 moves.

三個Ｘ則是十三步。

That’s a bad sign if it continues—

如果後續都是這種模式， 那可不妙了——

however many crosses you carve, Loki could choose the turn order and win.

不論你刻多少個Ｘ，

洛基都能靠決定由誰先開始來獲勝。

But this pattern doesn’t necessarily mean that every game is fixed—

但這個模式並不表示 每場遊戲的結果都已經注定——

perhaps 10 or 15 or 100 crosses has some winnable condition.

也許十個、十五個，或一百個Ｘ的 情況下會出現可獲勝的條件。

So let's try to understand what's happening.

所以，我們試著了解一下狀況。

We can start by looking at the final states of a few games.

我們可以先來看看 幾場遊戲的最終狀態。

As chaotic as they seem, there’s something interesting here.

雖然看起來很亂， 但卻內含有趣的資訊。

Every game ends with a number of distinct regions,

每場遊戲結束時， 都會劃分出數個不同的區域，

each with exactly one line poking in.

每個區域都只有一條線伸進去。

The one cross game has four— these three, and the one outside the blob.

一個Ｘ的遊戲有四個區域—— 這三個區域及最外部的區域。

Two crosses produces eight regions, and three crosses, 12.

兩個Ｘ會有八個區域， 三個Ｘ則是十二個區域。

That makes sense;

那是合理的，

each cross started with exactly four points that we could carve from—

每個Ｘ在開始時，都有 四個端點供我們刻連線——

we can think of those as lives.

我們可以把四個端點想成是四條命。

Each turn removes two ends, then adds two more.

每一回合會用掉兩個端點，

接著再增加兩個端點。

But when one is stuck by itself in an enclosure,

但當一個端點單獨被圍起來時，

it’s unusable and we lose a life.

它就沒有用了，我們就失去一條命。

By the end of the game

遊戲結束時，

all but one of those lives has been claimed by an enclosed shape,

每一條命都會被一個封閉的 形狀圍起來，只有一條命除外，

with the last poking out into the great blank beyond.

就是最後一條命， 它是伸向最外部的區域。

And when do we make an enclosed shape? Almost always.

而我們何時會製造出封閉的形狀？

幾乎每次都會。

In this game, we closed one off there, and there, and there.

在這場遊戲中，我們 在那裡製造一個封閉形狀，

接著是那裡，再來是那裡。

Sometimes they immediately claim a life,

有時，它們馬上就會奪走一條命，

but sometimes it happens later to two at once,

但有時，會晚點才發生， 一次奪取兩條命，

like when we divide a region in half.

比如把一個區域切成一半時。

But even that move added one more region than we previously had—

但就算是那種連線方式，也會讓 我們原本的區域數目再加一——

we turned one into two.

一個區域被切成兩個。

The only time we don’t create a new enclosure

只有一種情況不會 製造出新的封閉形狀，

is when we connect two separate clusters, like this.

那就是把兩個分開的群組 連結起來，像這樣。

A cluster might involve a single cross or a blob that’s formed around multiple.

群組可能只是一個Ｘ， 也可能是由多個Ｘ形成的區塊。

We never end up with an enclosed region without a line,

最後絕對不會留有 一個沒有線段的封閉區域，

because whenever we make a region, we carve a new segment,

因為每當我們製造出一個區域時 就會畫一新的線段，

half of which pokes in.

該線段有一半會伸向區域內。

We also never end with a region with multiple lines,

最後也不可能會留有 一個有數條線段的區域，

because then we could connect them and divide the region further.

因為如果有的話，就可以連結 這些線段再進一步劃分該區域。

So back to the single cross game.

所以，回到單一個Ｘ的遊戲。

We start with four lives in one giant region.

一開始有四條命， 全在一個巨型的區域中。

After we carve the first line, we have two regions.

連結出第一條線之後， 就有兩個區域了。

After the second line, three regions.

第二條線之後，會有三個區域。

And after the third, four, so we’re done.

第三、第四條線之後，就結束了。

Adding a second cross gives us four more lives,

再加上第二個Ｘ， 會讓我們多出四條命，

and also a free move that doesn’t make an enclosure,

也可以進行一次不會形成 封閉形狀的自由連線，

whenever we choose to connect these two clusters.

只要選擇連結這兩個群組即可。

The third cross adds four more lives and another free move.

第三個Ｘ又會添加四條命 和另一次自由連線的機會。

So that’s why the total number of turns goes up by five each time—

那就是為什麼總回合數 每次都會增加五——

four extra lives plus one free move.

四條額外的命和一次自由連線。

All of which is to say: Loki, true to form, has rigged the game.

總而言之，一如往常， 洛基操控了這個遊戲。

The only way to win is to trick the trickster...

要贏，只有一個辦法： 用惡作劇來對付惡作劇高手……

and there is something he overlooked.

而他確實有疏漏掉的地方。

Let's say you carve one cross.

假設你刻了一個Ｘ。

Loki chooses to go first, anticipating a quick and easy win on turn three.

洛基決定由他先開始，

他預期很快就能 在第三回合輕鬆獲勝。

So when, on your first move,

所以，當你第一次連線時，

you carve a line all the way to the last letter in your name,

你要把線一路連結到 你名字的最後一個字母，

his triumphant sneer passes through shock, dismay, and rage.

他得意的冷笑逐漸轉為 震驚、不安和憤怒。

But rules are rules, and a cross is a cross.

但規則就是規則，

Ｘ就是Ｘ。