Can you solve the magical maze riddle? - Alex Rosenthal

譯者: Lilian Chiu 審譯者: Esther Lam

Today is the annual Sly Wizard Tournament featuring competitors

今天是一年一度的狡猾巫師錦標賽，

其參賽者來自魔法世界裡 三所最棒的學校，

from the wizarding world’s three greatest schools,

and you’ve been entrusted with an enormous responsibility.

你被賦予了一個重大的責任。

You are to administer the tournament.

你負責主持這場錦標賽。

First, you and you alone will determine how many events there will be

首先，你得自己一個人決定 錦標賽中要有多少比賽的場次，

and their scoring system.

及其計分方式。

Then the three wizards will enter your maze

接著，三名巫師會進入你的迷宮，

and compete in your chosen events in utmost secrecy;

在你設定的比賽中競爭，一切保密進行；

only you and they will see what happens.

只有你和他們知道發生了什麼事。

The competition begins and...

比賽開始，……（八小時後）

Wow, that was one for the record books.

哇，這真是創下紀錄的比賽。

The winner was... wait, you have no idea.

獲勝的是……等等，你毫無頭緒。

The last thing you remember was a dark wizard showing up

你最後的記憶是有個黑暗巫師出現，

and casting a forgetting curse.

並施展了遺忘詛咒。

The competitors seem even more confused— each is convinced they won.

參賽者似乎比你更混淆——

每個人都相信自己贏了。

This is bad.

這很不妙。

There can be no do-overs,

不能重新比一次，

and the last failure to declare a winner set off the first Great Wizarding War.

而上回沒有宣佈贏家的結果 就是造成第一次魔法世界大戰。

You’ve got to figure this out— and fast.

你得設法找出贏家——且要快。

But for the life of you, you can’t remember a thing.

但你怎麼想就是什麼都想不起來。

You know you had to follow a few rules:

你知道你必須遵循一些規則：

there had to be three or more events, each with a single winner and loser.

比賽必須包含三場或更多，

每場都要有一名贏家和一名輸家。

Every event used the same scoring system,

所有比賽都要用相同的計分方式，

where first place received more points than second,

第一名的得分要比第二多，

and second more than third.

第二名要比第三名多。

All points were positive integers.

所有得分都是正整數。

Maybe there’s a record somewhere... oh, of course, your scorecard.

也許在哪裡會有記錄……

哦，當然，你的計分卡。

Well, that leaves something to be desired.

嗯，那還有所不足。

All that you wrote down was that in Calchemy,

你寫下的只有，在「煉金術賽」中，

Newt-niz won, Leib-ton took second,

紐特尼茲贏了，萊布頓位居第二，

and that was the only time Magnificent Marigold’s Magical Macademy

這一整天，華麗金盞花魔法 學院只有在這一場比賽吊車尾。

got third all day.

Oh, and some final scores:

哦，你還寫下了一些最終得分，

one school got 22 points, and both of the others got 9.

有一所學校得到二十二分，

另外兩所學校得到九分。

Why are you so bad at taking notes?!

你的筆記怎麼做的這麼糟糕？

No time for self-recrimination.

沒時間自責了。

The wizarding world is waiting.

魔法世界正在等待結果。

Who won the tournament?

誰贏了錦標賽？

Pause here to figure it out yourself. Answer in 3

要自行解題，在此暫停。 答案公佈倒數：三。

Answer in 2

答案公佈倒數：二。

Answer in 1

答案公佈倒數：一。

At first, it may seem like there are an overwhelming number

乍看之下，似乎有 非常多可能的計分方式。

of possible scoring systems,

so let's see if we can narrow our options.

咱們來看看能否減少可能的選項。

We can start by looking for clues in the total scores.

我們可以從總分中的線索著手。

Every event was scored the same way,

每場比賽的計分方式都相同，

so the sum of all points in the entire tournament

因此整個錦標賽的總得分

must be a multiple of one event’s total.

一定是單場比賽總得分的倍數。

In other words, if there were three events that scored 3, 2, 1,

換言之，

如果有三場比賽， 得分分別為三、二、一，

which adds up to 6, the total points for the day would be 18,

加起來等於六，

那天的錦標賽總得分就會是十八，

which is three events times 6 points.

因為三場比賽乘以六分等於十八。

Our total is 40.

我們的總得分是四十。

So we can make a table of possibilities: one event totaling 40 points,

因此，我們可以把 所有可能性製成表格：

總共一場比賽，總分四十分，

two totaling 20, four totaling 10, and so on.

二場比賽，總分各二十分； 四場比賽，總分各十分等等。

We know there were at least three events, which eliminates these options,

我們知道至少要有三場比賽， 所以可以刪除這些選項，

and we can also get rid of events with fewer than 6 points,

我們也可以刪掉比賽總分 少於六分的組合，

because the smallest possible total is 3 plus 2 plus 1.

因為比賽總分最少要是三加二加一。

That leaves two prospects.

可能性就只剩下兩個。

Let’s try to narrow those further by breaking down the possible points

咱們來分解每場比賽中取得的 分數，來進一步刪減可能的選項：

earned in each event:

if first place received 7 points,

如果第一名得到七分，

the teams that had totals of 9 couldn’t have won an event

總分得到九分的隊伍不可能 有在任何一場比賽獲勝，

because their total score would be 10 or more.

要不然它們的總分就會是十分以上。

That means the team with 22 would have to have won all four.

那就表示得分二十二分的隊伍 在四場比賽中都獲勝。

But then their total would be 28, so we can eliminate that option.

但該隊的總分就會是二十八分， 所以這個選項可以刪除了。

And with four events, these numbers can't be made to add up to 22.

如果是四場比賽，這些數字 不可能加總為二十二。

Finally, if first place got 5 points,

最後，如果第一名得到五分，

the highest possible score with four events would be 20,

四場比賽能得到的分數， 最多是二十分，

getting rid of these two as well.

這兩個選項也可以刪除了。

In fact, five events scoring 4 each could only reach 20 as well.

事實上，在五場比賽都取得 四分，總分也只有二十分。

That leaves us with just one possibility:

剩下的可能性就只有一個：

five events each scored 5, 2, 1.

五場比賽，各名次的得分 為五分、二分、一分。

There’s exactly one way to make those scores add up to 22:

要讓這些得分加起來等於 二十二分，只有一種組合：

the winner finished first four times and second once.

贏家在四場比賽得到 第一名，一場比賽得到第二名。

The scores of 9 mean one team won once and lost four times,

總分九分意味著有一隊 贏了一場比賽，輸了四場比賽；

and the other lost once and took second four times.

另一隊輸了一場， 另外四場拿到第二名。

That must be Marigold’s Macademy,

那一定是金盞花學院，

whose only third place finish was Calchemy based on your note.

根據你的筆記，該隊只有 在煉金術比賽中得到第三名。

And Leib-ton’s second place finish in Calchemy means they scored 22

萊布頓在煉金術比賽中得到第二名

表示該隊的總分是二十二分，

and won the Sly Wizard Tournament.

贏得了狡猾巫師錦標賽。

You have just enough evidence to prove it, keep your job, and avert war.

你有足夠的證據來證明該隊獲勝，

保住了你的飯碗，還避免了戰爭。

Phew!

呼！