Can you solve the trickster god riddle? - Alex Rosenthal

翻译人员: Marie Li 校对人员: Bruce Wang

Ragnarok has been raging for far too long;

诸神黄昏已经肆虐太久了；

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

许多神和英雄倒下了， 剩下的人只能勉强站起来。

Loki, his bright eyes dimmed by exhaustion,

洛基明亮的眼睛因疲惫而黯然失色，

asks to meet.

他要求见面。

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

他建议你和他在刻有你们名字的

atop a sacred table engraved with your names.

神圣桌子上玩游戏来解决冲突。

It has the following rules:

它有以下规则：

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

一名玩家将在桌子上 雕刻任意数量的十字架，

then play begins.

然后游戏开始。

Each turn, the active player must carve a line

每回合，主动玩家必须在不触及自己 或另一条线的情况下，

connecting two open ends without touching itself or another line.

雕刻一条连接两个开放端点的线。

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

然后，他必须在这条新线上切出一小段，

and pass the knife to the other player.

然后把刀传给另一个玩家。

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

只有交叉和回合结束部分是有效的。

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

谁走到最后一步，谁就赢了， 谁就会统治新世界。

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

洛基会让你在桌子上刻多少个十字架都可以，

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

然后他会选择先手还是后手。

You’re certain the trickster is up to something,

你肯定是这个骗子是在搞鬼

so how can you beat him?

那你怎么能打败他呢？

Pause here to figure it out yourself. Answer in 3

在这里暂停一下视频，自己想想。 答案在3秒后揭晓

Answer in 2

2秒

Answer in 1

1秒

Often the best way to analyze a game like this—

通常是最好的分析方法像这样的游戏是—

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

是约翰·康威发明的 以球芽甘蓝的名字命名

is to try it out.

就是尝试一下

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

让我们从最简单的例子开始： 一个单一的十字。

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

在这里，不管我们怎么玩， 这个游戏总会以三步棋结束。

With two crosses, the game always ends in eight.

有两个十字时， 游戏总是以8回合结束。

And with three crosses, 13 moves.

三个十字，13步。

That’s a bad sign if it continues—

如果这种情况继续下去， 那将是一个不好的迹象

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

不管你刻了多少十字， 洛基可以选择回合顺序并获胜。

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

但这种模式并不一定意味着 每场比赛都是固定的

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

也许是10个、15个或100个十字 有一些可赢的条件。

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

让我们试着去理解发生了什么。

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

我们可以观察一下一些游戏的最后状态。

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

虽然看起来很混乱， 但这里有一些有趣的东西。

Every game ends with a number of distinct regions,

每场比赛都以一个数字结束不同的区域，

each with exactly one line poking in.

每个都有一个线插入。

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

一个交叉游戏有四个-这三个， 还有一个在块的外面。

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

两个十字架产生八个区域， 三个叉，就是12个。

That makes sense;

这是有道理的；

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

每个十字都是从4点我们可以连接

we can think of those as lives.

我们可以把它们看作是生命。

Each turn removes two ends, then adds two more.

每转一圈去掉两头，然后再加两个。

But when one is stuck by itself in an enclosure,

但当一个点被困在一个圈里时，

it’s unusable and we lose a life.

它将无法使用，我们失去了一条生命。

By the end of the game

在比赛结束前

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

除了一个点，其他的都是 被关在一个圈里，

with the last poking out into the great blank beyond.

最后一根线伸到远处一片空白。

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

什么时候我们会形成一个 封闭的形状呢？几乎总是。

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

在这个游戏中，我们在 这里关闭了一个，这里，和这里。

Sometimes they immediately claim a life,

有时他们会立即夺去一条生命，

but sometimes it happens later to two at once,

但有时它会在后面同时失去两条命，

like when we divide a region in half.

就像我们把一个区域分成两半。

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

但即便是这一举动， 也增加了一个比之前的区域要大

we turned one into two.

我们把一个变成了两个。

The only time we don’t create a new enclosure

我们唯一不创造一个新的圈时，

is when we connect two separate clusters, like this.

就是当我们连接两个独立的点，像这样。

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

一个簇可能包含一个十字 或者是围绕多个点形成的一团。

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

我们永远不会得到一个 封闭的没有线的区域，

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

因为无论何时我们建立一个区域， 我们刻下了一个新的线，

half of which pokes in.

其中一半被圈了进去。

We also never end with a region with multiple lines,

我们也不会以区域内有多条线结束。

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

因为这样我们就可以把它们 连接起来并进一步划分区域。

So back to the single cross game.

回到单交叉的游戏。

We start with four lives in one giant region.

我们从四条生命开始在一个巨大的地区。

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

我们刻好第一条线之后， 我们拥有两个区域。

After the second line, three regions.

在第二条线之后，三个区域。

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

第三个之后，四个，完成了。

Adding a second cross gives us four more lives,

再加上第二个叉再多四条命，

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

还有一个自由的行动不会形成一个圈，

whenever we choose to connect these two clusters.

无论何时我们选择连接这两个集群。

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

第三个十字都会增加 四条生命和一个自由行动。

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

这就是为什么总圈数每次都是增加5

four extra lives plus one free move.

四条命加一次自由行动。

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

所有这些都是在说： 洛基一如既往地操纵了比赛。

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

赢的唯一方法是去骗骗子……

and there is something he overlooked.

这有对象他忽略了。

Let's say you carve one cross.

假设你刻了一个十字。

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

洛基选择先走， 满怀期待在第三回合轻松取胜。

So when, on your first move,

所以当你第一次行动时，

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

你划了一条线一直到 你名字的最后一个字母，

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

他得意的冷笑变成了震惊、沮丧和愤怒。

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

但规则就是规则，十字就是十字。