Can you solve the Trojan War riddle? - Dennis E. Shasha

譯者: 至磊Zi Le 黃Ng 審譯者: Amanda Zhu

The Trojan War has been raging for 10 years,

特洛伊戰爭已經打了十年，

with neither Greeks nor Trojans prevailing.

希臘人和特洛伊人勢均力敵。

Gods and humans alike are desperate for a break,

神祇和人類都渴望休戰，

so when a divine omen races across the sky,

所以當天上出現了一個異兆，

the two sides agree to a 10 day truce.

雙方便同意休戰十天。

From high up on Olympus you’ve been waiting for an opportunity

在奧林帕斯山上，

你正等待機會終結這場血腥的戰爭。

to bring this bloody war to its conclusion.

When you go to consult the Fates, they advise:

你向命運三女神諮詢，她們說：

should the peace last for a full 10 days, all will end soon.

如果和平能維持整整十天， 戰爭很快就能結束。

However, if the truce is broken,

然而，如果停戰協議被破壞，

the ensuing battle will lead to 10 more devastating years of war.

後續戰役將使慘痛的戰爭延續十年。

The Fates’ loom has shown them the exact conditions

命運三女神的絲線顯示了

that will keep the truce intact.

維持休戰的確切條件。

The great Trojan plain can be viewed as a grid of Greek and Trojan encampments.

希臘和特洛伊在廣大的特洛伊平原上 以網格的排列方式紮營，

If they’re organized in such a way that any Greek can reach any other Greek camp

如果紮營的方式使希臘人 不必經過特洛伊營地

without having to pass through a Trojan camp, and likewise for Trojans,

就能前往彼此營地，

而特洛伊人亦如此紮營，

plus neither side completely surrounds the other, peace will prevail.

且沒有一方被四面包圍， 和平就能維持。

Anyone can move to a horizontally or vertically adjacent camp,

每個人都可以移往 前後左右相鄰的營地，

but never diagonally.

但不能走對角線。

The problem is, they’re currently arranged like this.

問題是他們目前如此排列。

Tonight, you can use your powers to swap up to six pairs of camps

今晚，你可以利用你的力量 對調最多六對營地，

that are horizontally, vertically, or diagonally adjacent.

每一對必須是前後左右或斜向相鄰。

No camp can be moved more than once.

一個營地只能動一次。

Which swaps do you make to keep the peace?

要保持和平，你會怎麼對調？

Pause here to figure it out yourself. Answer in 3

［要自己想請按暫停 三秒後解答］

Answer in 2

［兩秒後解答］

Answer in 1

［一秒後解答］

The first insight here is to divide this into two sub-problems.

第一項重點是將其切成兩個子問題。

There’s the matter of connecting 4 clumps of Greeks

一個問題是要連結四大塊希臘營地，

without putting holes in the Trojan line.

但不要截斷特洛伊營地。

And then there’s dealing with the thorny center space.

然後要處理正中央的棘手營地。

Let’s consider the Greeks first.

我們先思考希臘營地。

To connect any Greek clumps,

要連結任一塊希臘營地，

you’ll have to mess with the nice, straight Trojan lines.

就必須打亂漂亮的特洛伊直線。

If you try to do that anywhere in the center of these arms,

如果你調動接近中心的特洛營地，

you'll create new isolated clusters of Trojans.

就會製造出一塊孤立的特洛伊營地。

So the only option is to go to the perimeter of the field

所以唯一的選項是到邊緣，

and move some Trojans diagonally, say here, here, and here.

斜向移動一些特洛伊營地， 例如 1、2、3。

Now for the center.

現在來到中央。

there’s no way to connect the Trojan arms without swapping a Trojan in.

如果不把特洛伊營地換到中央， 就不能連接特洛伊的四條營地。

But continuing to shift that arm of Trojans inward

但如果繼續將這一條 特洛伊營地移進來，

would require moving the same Greek camp multiple times.

就需要重複移動相同的希臘營地。

However, you could shift the whole Trojan arm up and to the right,

然而你可以移動整條 特洛伊營地到右上方，

closing this gap.

把缺口補起來。

There are several solutions with slight variants,

有幾種稍稍不同的解法，

but as long as you perform this maneuver on the short arm of Trojans,

但只要如此移動最短的 那條特洛伊營地，

you can achieve peace in exactly 6 moves.

就剛好可以用六個動作達成和平。

You make the swaps and all is well until the fifth night.

你做了這些對調， 一切安好，直到第五晚。

One of your rival gods wants to see the bloodshed continue,

一個和你為敵的神祇 想繼續看到殺戮，

and has taken advantage of a forgotten prophecy.

便利用一項被遺忘的預言。

He’s convinced one Trojan camp to make a swap

他說服某個特洛伊營地

與其前後左右或斜向的 希臘鄰居對調，

with their horizontal, vertical, or diagonal Greek neighbors

that will break up the Greek connectivity.

這將會打斷希臘營地的連接。

Once again, you consult the Fates, who prophesize the following:

你再次諮詢命運三女神， 她們如此預言：

the meddling Trojan camp is somewhere within four grid spaces

多管閒事的特洛伊營地位於 戰場邊緣的四塊區域。

of the perimeter of the battlefield.

They won’t go through with a swap if it only breaks up Trojan connectivity.

若只打斷特洛伊營地， 那個營地就不會想對調。

And finally, you can make at most two swaps

最後，你至多可以再對調兩次，

with the same rules as before to thwart them.

規則和先前一樣。

Which swaps do you make to block the troublesome Trojan camp?

你要怎麼對調來阻止 惹事的特洛伊營地？

Answer in 3

［三秒後解答］

Answer in 2

［兩秒後解答］

Answer in 1

［一秒後解答］

You won't be able to identify the scheming camp precisely,

雖然你無法準確地找出是哪個營地，

but there’s a lot you can do to at least narrow down the options.

但還是可以做很多事情， 起碼能篩選出可能的選項。

They have to be somewhere in this area.

他們一定是在打叉外的區域裡，

And they have to be able to block Greek camps from each other in a single swap.

而且他們必須只對調一次 就隔開希臘營地。

That doesn’t leave many options;

這些條件下的選項不多了。

the only possible blockages are at the end of these two arms,

可能的特洛伊營地 必定落在這兩條的尾部，

where a Trojan camp could plug a hole without opening a new one.

才能截斷希臘營地， 而且不會截斷自己的營地，

So they must be in one of these four camps.

所以必定是這四個營地之一。

Let’s look at the right arm first.

我們先看右邊這兩個。

There’s a threat here because this column has two Trojan camps.

這一直行有兩個特洛伊營地， 所以具有威脅。

If one moves to the right, the other will still be in place,

如果一個右移，

另一個仍會在原地阻擋希臘人穿越，

blocking Greeks from crossing.

so we can thwart them by moving either one a column left into this square.

所以我們可以把其中之一 往左移動一行，到這個格子。

and the same principle applies to the bottom arm.

同樣的原則也適用於 下方的兩個營地。

Your effort maintains the peace for the final 5 days.

你的努力維持住最後五天的和平。

But it seems that a certain Greek general noticed what was happening

但看起來一位希臘將軍 注意到這些事，

and left the Trojans a parting gift...

留給特洛伊人一份告別禮物……