Lightning calculation and other "mathemagic" | Arthur Benjamin

譯者: Wang Qian 審譯者: Zachary Lin Zhao

Good morning, ladies and gentlemen.

各位女士先生們 午安

My name is Art Benjamin, and I am a "mathemagician."

我的名字是 亞瑟 班傑明, 而且我是一位"數學魔術師".

What that means is, I combine my loves of math and magic

我結合了我的兩個最愛, 數學還有魔術

to do something I call "mathemagics."

創造了我稱的 "數學魔術"

But before I get started, I have a quick question for the audience.

在我開始之前, 我有一個簡單的問題

By any chance, did anyone happen

在觀眾之中

to bring with them this morning a calculator?

有沒有人剛好帶了計算機?

Seriously, if you have a calculator with you, raise your hand.

說真的, 要是你有帶計算機的話請舉手, 舉手.

Raise your hand. Did your hand go up?

我 - 你剛剛有舉手嗎?

Now bring it out, bring it out. Anybody else?

好 拿出來, 拿出來. 還有其他人嗎?

I see, I see one way in the back.

我看看, 我看到後方還有一位.

You sir, that's three.

就是妳先生, 這樣就有三位了.

And anybody on this side here?

在這一邊有人嗎?

OK, over there on the aisle.

好的, 在走道邊的那一位. 請你們四位

Would the four of you please bring out your calculators,

帶著你們的計算機, 帶著它們到台上.

then join me up on stage.

Let's give them a nice round of applause.

請幫這些自願者鼓掌.

(Applause)

(掌聲)

That's right.

沒錯. 好的, 我還沒有機會

Now, since I haven't had the chance to work with these calculators,

使用這些計算機, 所以我必須確定

I need to make sure that they are all working properly.

他們使用上都沒有問題.

Would somebody get us started by giving us a two-digit number, please?

有沒有人可以先給我們一個開始

給我一個2位數的號碼?

How about a two-digit number?

2位數的號碼好嗎?

Audience: 22.

觀眾: 22

AB: 22. And another two-digit number, sir?

班傑明: 22. 先生, 再另一組2位數好嗎?

Audience: 47.

觀眾: 47

AB: Multiply 22 times 47, make sure you get 1,034,

班傑明: 22 乘與 47, 確定你的答案是 1,034.

or the calculators are not working.

不然你的計算機就是有問題的. 你的都算到 1,034? 1,034?

Do all of you get 1,034? 1,034?

Volunteer: No.

女: 不是.

AB: 594. Let's give three of them a nice round of applause there.

班傑明: 594. 我們給他們其中三位掌聲鼓勵.

(Applause)

(掌聲)

Would you like to try a more standard calculator, just in case?

你想不想試試一個比較標準的計算機, 以防萬一?

OK, 好的.

OK, great.

What I'm going to try and do then --

我現在要嘗試做的就是 --

I notice it took some of you a little bit of time to get your answer.

我發現你們需要滿長的一段時間來計算.

That's OK.

那沒問題. 我來教你們一個計算機

I'll give you a shortcut for multiplying even faster on the calculator.

算成法的捷徑.

There is something called the square of a number,

一個數字的平方

which most of you know is taking a number and multiplying it by itself.

你們大多都知道 就是

把一個數字來乘與它自己

For instance, five squared would be?

比方說, 5 的平方是?

Audience: 25.

觀眾: 25

AB: 25. The way we can square on most calculators --

班傑明: 25. 現在, 我們在計算機上算平方的方式是 --

let me demonstrate with this one --

讓我用這一個來示範 --

is by taking the number, such as five,

先把一個數字, 例如 5,

hitting "times" and then "equals,"

按下 "乘與" (x) 然後再按 "等於" (=),

and on most calculators that will give you the square.

然後大多數 計算器會算出平方。

On some of these ancient RPN calculators,

在一些比較舊的 RPN 計算機上,

you've got an "x squared" button on it,

你會有 X^2 (X的平方) 的按鈕,

will allow you to do the calculation even faster.

就可以更快的計算出平方.

What I'm going to try and do now is to square, in my head,

現在我要嘗試做的就是用心算

four two-digit numbers

算出四組兩位數的數字的平方

faster than they can do on their calculators,

比他們用計算來計算得還要快, 即使使用捷徑.

even using the shortcut method.

What I'll use is the second row this time,

這次我找第二排, 請你們四位 --

and I'll get four of you

一, 二, 三, 四 -- 各喊出一組兩位數的數字,

to each yell out a two-digit number,

and if you would square the first number,

然後請你算出第一組的平方,

and if you would square the second, the third and the fourth,

再來你算出第二組的平方, 再來第三和第四,

我試著和你們比賽看誰比較快, 好嗎?

I will try and race you to the answer. OK?

So quickly, a two-digit number please.

快一點 -- 一組兩位數數字.

Audience: 37.

觀眾: 37

Arthur Benjamin: 37 squared, OK.

班: 37 平方, OK.

Audience: 23.

觀眾: 23

AB: 23 squared, OK.

班: 23 平方, OK.

Audience: 59.

AB: 59 squared, OK, and finally?

觀眾: 59

班: 59 平方, OK, 再來最後

Audience: 93.

觀眾: 93

AB: 93 squared.

Would you call out your answers, please?

班: 93 平方. 請你們說出你們的答案

Volunteer: 1369. AB: 1369.

女: 1369 班: 1369

Volunteer: 529. AB: 529.

女: 529

班: 529

Volunteer: 3481. AB: 3481.

男: 341

班: 3481

Volunteer: 8649.

男: 8649

AB: Thank you very much.

班: 非常謝謝你們.

(Applause)

(掌聲)

Let me try to take this one step further.

現在讓我來試著更進一步

I'm going to try to square some three-digit numbers this time.

這一次我要試著平方一些三位數

I won't even write these down --

我甚至不把它寫下來

I'll just call them out as they're called out to me.

我直接在數字喊出來之後說出答案

Anyone I point to, call out a three-digit number.

我手指指到誰, 就請喊出一組三位數

Anyone on our panel, verify the answer.

在台上的人請幫我確認我的答案

Just give some indication if it's right.

請讓我知道我計算的是否正確

A three-digit number, sir, yes?

先生, 一組三位數?

Audience: 987.

觀眾: 987

AB: 987 squared is 974,169.

班: 987 平方是 974,169

(Laughter)

(笑聲)

AB: Yes? Good.

對嗎? 很好

Another three-digit --

再來, 在一組三位數 --

(Applause)

(掌聲)

先生, 再一組三位數?

-- another three-digit number, sir?

Audience: 457.

觀眾: 457

AB: 457 squared is 205,849.

班: 457 平方是 205,849

205,849?

205,849?

AB: Yes?

對嗎?

OK, another, another three-digit number, sir?

好的, 再一組三位數?

Audience: 321.

AB: 321 is 103,041.

觀眾: 321

班: 321 是 103,041. 103,041.

103,041.

對嗎? 請再多給我一組

Yes? One more three-digit number please.

觀眾: 722

Audience: Oh, 722.

AB: 722 is 500, that's a harder one.

班: 722 是 500 -- 這一組比較困難

Is that 513,284?

是 513,284 嗎?

Volunteer: Yes.

女: 沒錯

AB: Yes? Oh, one more, one more three-digit number please.

班: 對嗎? 再一組, 請再給我一組

Audience: 162.

觀眾: 162

162 squared is 26,244.

162 平方是 26,244

Volunteer: Yes.

非常謝謝你們.

Thank you very much.

(Applause)

(掌聲)

(Applause ends)

Let me try to take this one step further.

現在讓我來再進一步

(Laughter)

(笑聲)

I'm going to try to square a four-digit number this time.

我要試著來平方四位數的數字

You can all take your time on this;

現在你們可以慢慢來, 我不會比你們還要快算出答案

I will not beat you to the answer on this one,

但是我會盡量給你正確的答案

but I will try to get the answer right.

這次為了更加隨機, 讓第四排的觀眾

To make this a little bit more random, let's take the fourth row this time,

就說.. 一, 二, 三, 四

let's say, one, two, three, four.

If each of you would call out a single digit between zero and nine,

你們四位一人說出一位數

組成一組四位數讓我來平方

that will be the four-digit number that I'll square.

觀眾: 9

Nine.

班: 9

Seven.

觀眾: 7 班: 7

Five.

觀眾: 5 班: 5

觀眾: 8 班: 8

Eight.

9,758, this will take me a little bit of time, so bear with me.

9758, 這需要一點時間

95 million --

95,218,564?

(Sighs)

218,564?

Volunteer: Yes!

女: 正確

AB: Thank you very much.

班: 非常謝謝

(Applause)

(掌聲)

(Applause ends)

Now, I would attempt to square a five-digit number --

現在, 讓我來平方一個五位數

and I can --

我可以

but unfortunately, most calculators cannot.

但是大部分的計算機不行

(Laughter)

(笑聲)

Eight-digit capacity -- don't you hate that?

八位數的限制 -- 真是麻煩

So, since we've reached the limits of our calculators --

既然我們到了計算機的極限了 --

what's that?

甚麼? 你的計算機可以到幾位數?

Does yours go higher?

女: 我不知道

班: 可以超過八位數嗎?

Volunteer: I don't know.

AB: Oh, yours does?

你的可以嗎?

Volunteer: I can probably do it. AB: I'll talk to you later.

男: 我的或許可以

班: 我晚點再跟你談談

In the meanwhile, let me conclude

現在在第一段結束之前

the first part of my show by doing something a little trickier.

讓我來用些更巧妙的把戲來小結 我的第一部 分表演。

Let's take the largest number on the board here, 8649.

讓我們用這塊板上最大的一個數字，8649。

Would you each enter that on your calculator?

你們每個人可否在計算器上輸入這個數？

And instead of squaring it this time,

這次不要平方，

I want you to take that number and multiply it

我要你們用那個數乘以

by any three-digit number that you want,

任何3位數，

but don't tell me what you're multiplying by --

但不要告訴我你所乘的數 --

just multiply it by any random three-digit number.

只要乘以任何一個3位數。

So you should have as an answer either

那麼你得到的答案可能會是

a six-digit or probably a seven-digit number.

一個六位數或者七位數。

How many digits do you have, six or seven?

你的是幾位，6還是7？

Seven, and yours?

7，你的呢？女士：7。

Seven? Seven?

阿 瑟：7？7嗎？

不確定。

And, uncertain.

Seven.

男士：是的。

Is there any possible way that I could know

亞瑟: 7。 有沒有辦法會讓我知道

what seven-digit numbers you have?

你所得到的7位數？應該不可能。

Say "No."

(Laughter)

（笑聲）

Good, then I shall attempt the impossible --

很好。那我應該來挑戰下這個不可能 --

or at least the improbable.

至少看上去是不太可能的事。

What I'd like each of you to do is to call out for me

接下來我想讓你們告訴我

any six of your seven digits, any six of them,

7位元數裏面的任意6位元數字。

in any order you'd like.

任意順序都可以。

(Laughter)

（笑聲）

每次一位數，我會試著算出剩下的數。

One digit at a time,

I shall try and determine the digit you've left out.

那麼，從你開始吧。

Starting with your seven-digit number,

請喊出任意6位元數字。

call out any six of them please.

Volunteer: 1, 9, 7, 0, 4, 2.

女士：1， 哦，197042。

AB: Did you leave out the number 6?

亞瑟：你是不是漏說了6？

Good, OK, that's one.

女士：是的，亞瑟:很好，好的，沒錯。

You have a seven-digit number, call out any six of them please.

你的是7位數，請大聲說出其中任意的六個數。

女 士：44875。

Volunteer: 4, 4, 8, 7, 5.

亞瑟: 我好像只聽到5個數位。我 -- 等下 -- 44875 --

I think I only heard five numbers. I -- wait -- 44875 --

did you leave out the number 6?

你是不是漏說了數字6？

Same as she did, OK.

女士：是的。 亞瑟:跟她的一樣，好的。你得到的是一個7位數 --

You've got a seven-digit number --

大聲清晰地說出其中的任意6個數字。

call out any six of them loud and clear.

Volunteer: 0, 7, 9, 0, 4, 4.

男：079044.

I think you left out the number 3?

亞瑟:我想你漏說了數字3？

AB: That's three.

就是3. 要是我隨便猜到話，那麼我猜中其中4位元數字的概率

The odds of me getting all four of these right by random guessing

將會是萬分之一。10的負四次方。

would be one in 10,000: 10 to the fourth power.

OK, any six of them.

好了，任意6位元數字。

(Laughter)

Really scramble them up this time, please.

這次請把它們攪亂一下。

Volunteer: 2, 6, 3, 9, 7, 2.

男：263972。

Did you leave out the number 7?

亞瑟:你是不是漏說了數字7？

And let's give all four of these people a nice round of applause.

現在讓我們給這四位觀眾予熱烈的掌聲。

非常感謝。

Thank you very much.

(Applause)

(Applause ends)

我的下一個數 --

For my next number --

(Laughter)

（笑聲）

while I mentally recharge my batteries,

在給我腦袋充電期間

我有個問題要問下觀眾們。

I have one more question for the audience.

By any chance, does anybody here happen to know

有可能的話，在場的有誰剛好知道

the day of the week that they were born on?

你生日的那天是星期幾？

If you think you know your birth day, raise your hand.

如果你覺得知道的話，舉下手。

Let's see, starting with -- let's start with a gentleman first.

讓我們看看，從 -- 從男士開始，

What year was it, first of all?

好的先生， 先說下是哪一年？這就是為什麼我要先從男士開始。

That's why I pick a gentleman first.

哪年？

Audience: 1953.

觀 眾：1953。

1953, and the month?

亞瑟: 1953，哪個月？

November what?

觀眾：11 月。亞瑟：11月幾號？

觀眾:23 號。

23rd -- was that a Monday?

亞瑟: 23號 -- 是不是星期一？觀眾：是的。

Audience: Yes.

沒錯，很 好。還有人嗎？還有誰想要 --

Good. Somebody else?

I haven't seen any women's hands up.

呃，還沒， 我還沒看到有女士舉手。

OK, how about you, what year?

啊，很好， 你呢，哪年？

1949, and the month?

觀 眾：1949. 亞瑟: 1949， 哪月？

October what?

觀眾： 十月。亞瑟: 十月幾號？

觀眾： 5號。

Fifth -- was that a Wednesday?

亞瑟: 5號 -- 那是不是星期3？

Yes! I'll go way to the back right now, how about you?

沒錯，現在我從後面選，你怎樣？

Yell it out, what year?

大聲說出來，哪年？觀眾：1959。

Audience: 1959.

1959, OK -- and the month?

阿 瑟:1959， 好的 -- 哪月？

觀眾：二 月。

Audience: February.

February what?

亞瑟: 2月幾號？ 觀眾：6號。

Sixth -- was that a Friday? Audience: Yes.

亞瑟: 6號，那是不是星期五？觀眾：是的。

Good, how about the person behind her?

很好，在她後面的那個人要不要試試？

Call out, what year was it?

喊出 -- 哪一年？

Audience: 1947. AB: 1947, and the month?

觀 眾：1947. 亞瑟: 1947，哪月？

Audience: May. AB: May what?

觀眾：5 月。亞瑟: 5月幾號？

Seventh -- would that be a Wednesday?

觀眾：7 號。亞瑟:7號 -- 那是不是星期三？

Audience: Yes. AB: Thank you very much.

觀眾：是的。

亞瑟:非常感謝。

(Applause)

（掌聲）

Anybody here who'd like to know the day of the week they were born?

在場的哪一位想知道自己的生日是在星期幾的？

We can do it that way.

我們也可以這麼做。

Of course, I could just make up an answer and you wouldn't know,

當然，這樣的話我亂編一個你也不會知道，

所以我事先有準備了下。

so I come prepared for that.

I brought with me a book of calendars.

我帶了一個日曆。

It goes as far back into the past as 1800, because you never know.

可以查回到1800年，誰知道會不會用得著呢？哈。

(Laughter)

（笑聲）

I didn't mean to look at you, sir -- you were just sitting there.

我不是故意看著你，先生 --

你只是恰巧坐在那邊。

(Laughter)

Anyway, Chris, you can help me out here, if you wouldn't mind.

不管怎樣，Chris,你可以幫我下，如果你不介意的話。

This is a book of calendars.

這是一本日曆，然後我會問 --

Who wanted to know their birth day?

是誰想知道他的生日的，是你嗎，先生？好的。

What year was it, first of all?

先問下哪一 年？

Audience: 1966.

觀 眾：1966。

66 -- turn to the calendar with 1966.

亞瑟: 66年 -- 翻到日曆的1966年 --

And what month?

亞瑟: 哪月？

Audience: April. AB: April what?

觀眾：4 月。 亞瑟: 4月幾號？

Audience: 17th.

觀眾：17 號。 亞瑟: 17號 -- 我確信那是個星期天。

I believe that was a Sunday.

Can you confirm, Chris?

你能否確認下，Chris？

Chris: 是的。亞瑟: 很好，我跟你說

Chris Anderson: Yes.

AB: I'll tell you what, Chris:

chris， 用你面前的那本書，

as long as you have that book in front of you,

do me a favor, turn to a year outside of the 1900s,

幫我下忙， 翻到1900s以外的，

either into the 1800s or way into the 2000s --

幫我下忙， 翻到1900s以外的，

that'll be a much greater challenge for me.

翻到頁面 1800s 或者2000s --那樣對我來 說會更有挑性。

AB: What year would you like? CA: 1824.

你喜歡哪年，Chris？

Chris: 1824.

AB: 1824, OK.

亞瑟: 1824, 好的。

AB: And what month?

哪月 呢？Chris: 六月。

CA: June.

哪月 呢？Chris: 六月

AB: June what? CA: Sixth.

AB: Was that a Sunday?

6號 -- 是不是星期天？

CA: It was. AB: And it was cloudy.

Chris: 沒錯。 亞瑟:並且是陰天。

(Laughter)

Good, thank you very much.

很好，非常感謝。

(Applause)

（掌聲）

(Applause ends)

But I'd like to wrap things up now

但是現在我想來個總結

by alluding to something from earlier in the presentation.

再次回到

我之前的表演

There was a gentleman up here who had a 10-digit calculator.

先前臺上有位帶10位數計算器的先生。

Where is he, would you stand up,

現在在哪裏，你能站起來一下嗎？

10-digit guy?

10位數的夥計？

OK, stand up for me just for a second,

好的，請站 起來下，

so I can see where you are.

好讓我可以 看到你在哪里。

You have a 10-digit calculator, sir, as well?

好，哦，好的 -- 你也有一個10位數的計算器？

OK, what I'm going to try and do, is to square in my head

很好，我接下來要做的是，心算平方

a five-digit number requiring a 10-digit calculator.

一個5位元數的數位，這需要個10位元數的計算器。

But to make my job more interesting for you, as well as for me,

為了給大家和我自己增加點樂趣，

I'm going to do this problem thinking out loud.

我會把心算過程

大聲的念出來。

So you can actually, honestly hear

這樣你們就可以實際上聽到

what's going on in my mind while I do a calculation of this size.

我心算時的具體過程

當我計算這樣大的數字的時候。

Now, I have to apologize to our magician friend Lennart Green.

現在，我得向我們的魔術師朋友 Lennart Green道下歉。

I know as a magician we're not supposed to reveal our secrets,

我知道作為一個魔術師本不應該洩漏我們的秘密，

but I'm not too afraid

但我並不是很擔心其他人

that people are going to start doing my show next week, so --

會在下個星期開始模仿我的表演，所以 --

I think we're OK.

我想沒有什麼問題。

(Laughter)

(Applause)

So, let's see,

那麼，讓我們開始吧，

let's take a different row of people, starting with you.

讓我們選另一排的觀眾，就從你開始吧。

I'll get five digits: one, two, three, four.

我將得到5位數：1，2，3，4 --

Oh, I did this row already.

哦，我已經選過這排了。那就選你前面的這排觀眾，

Let's do the row before you,

starting with you: one, two, three, four, five.

從你開始先生：1，2，3，4，5。

Call out a single digit --

（每個人） 喊出一個一位數 -- 這樣就組成一個5位元數的數字

that will be the five-digit number that I will try to square, go ahead.

我會心算這個數的平方。開始吧。

觀眾：5。 亞瑟：5。

Five.

Seven.

觀眾：7。 亞瑟：7。

觀眾：6。 亞瑟：6。

Six.

觀眾：8。 亞瑟：8。

Eight.

Three.

觀眾：3。 亞瑟：3。

57,683 --

57683

squared.

Yuck.

平方。慘啦。

Let me explain to you how I'm going to attempt this problem.

讓我來給大家解釋下

我接下來要怎麼算。

I'm going to break the problem down into three parts.

我會把這個問題分成3部分。

I'll do 57,000 squared,

我先算 57000的平方，

plus 683 squared,

然後加上 683的平方，

plus 57,000 times 683 times two.

加上 57000乘以

683乘以 2。

Add all those numbers together,

把所有的結果加起來，

and with any luck, arrive at the answer.

幸運的話， 就可以得出答案。

Now, let me recap.

現在，讓我先想一下（合上筆帽）。（一語雙關）

(Laughter)

Thank you.

謝謝。

(Laughter)

While I explain something else --

當我講一些其他的 --

(Laughter)

-- I know, that you can use, right?

-- 我知道，你可以利用這個，對吧？

(Laughter)

While I do these calculations,

當我心算的時候，在計算的過程中

you might hear certain words,

你會聽到某些詞語，

來對應一些數字，融入到計算當中。

as opposed to numbers, creep into the calculation.

Let me explain what that is.

讓我來解釋下是什麼。

This is a phonetic code,

這是語音代碼，

a mnemonic device that I use,

相當於一個記憶用的設備，

that allows me to convert numbers into words.

這個設備能幫我把數字轉換成單詞。

I store them as words, and later on retrieve them as numbers.

我先存為單詞，然後再轉回成數字。

I know it sounds complicated; it's not.

我知道這聽起來有點複雜；（實際上）一點也不 --

I don't want you to think you're seeing something out of "Rain Man."

我不想讓你們以為自己看到了‘雨人’。

（笑聲）

(Laughter)

There's definitely a method to my madness --

這其中絕對有種方法來解釋我瘋狂的表演 --

definitely, definitely.

一定的，一 定的。不好意思。

Sorry.

(Laughter)

（笑聲）

If you want to talk to me about ADHD afterwards,

如果你想找我談論小兒多動症的話，

you can talk to me then.

你可以找我談談。好吧 --

By the way, one last instruction,

順便提下，

for my judges with the calculators --

給我那個有計算器的裁判最後一個說明

you know who you are --

至少有一半的機會

there is at least a 50 percent chance that I will make a mistake here.

我會犯錯。

If I do, don't tell me what the mistake is;

如果算錯了，不要告訴我哪里錯了；

just say, "you're close," or something like that,

只要說， ‘接近了，’或者類似的，然後我會再試著算出正確的答案 --

and I'll try and figure out the answer --

這樣會更有趣點。

which could be pretty entertaining in itself.

If, however, I am right,

如果，我對了的話，

whatever you do, don't keep it to yourself, OK?

無論如何， 你都不要自己留著結果，好嗎？

(Laughter)

（笑聲）

Make sure everybody knows that I got the answer right,

確保讓大家知道我算對了，

因為這對我來說是個完美的收場。

because this is my big finish, OK.

So, without any more stalling,

好吧，閒話少說，

here we go.

我們開始吧。

I'll start the problem in the middle, with 57 times 683.

我會從問題的中間部分開始，先算57乘以683。

現在，57乘以68等於3400，加上476等於3876，

57 times 68 is 3,400, plus 476 is 3876,

那是 38760加上171，

that's 38,760 plus 171,

38,760 plus 171 is 38,931.

38760 加上171等於38931。

38,931; double that to get 77,862.

38931； 翻一倍得到77862。

77,862 becomes cookie fission,

77862 變成‘cookie fission’，

cookie fission is 77,822.

‘cookie fission’ 是77822。

That seems right, I'll go on. Cookie fission, OK.

好像沒錯， 繼續。'cookie fission’，好的。

Next, I do 57 squared, which is 3,249, so I can say,

接下來，我算57的平方等於3249，那麼應該是，

three billion.

30億。用249加上'cookie',249，

Take the 249, add that to cookie, 249,

oops, but I see a carry coming --

哦，但是我看到有一個包過來了 --

249 --

249 --

add that to cookie, 250 plus 77,

加上 'cookie'，250加上77，

is 327 million --

等於3億2千7百萬 --

fission, fission, OK, finally, we do 683 squared,

'fission, fission,' 好的，總算可以算683的平方了，

that's 700 times 666, plus 17 squared

相當於 700乘以666，再加上17的平方

is 466,489, rev up if I need it,

等於 466489，我需要的時候轉起來，

rev up, take the 466,

放大，用 466，

add that to fission, to get,

加上 'fission'，得到，

哦老天 --

oh gee --

328,489.

328489。

Audience: Yeah! AB: Good.

觀眾：沒錯！

亞瑟：很好。

Thank you very much.

（掌聲）

(Applause)

非常感謝。

I hope you enjoyed mathemagics.

希望你們能喜歡數學魔術。謝謝大家。

Thank you.

(Applause)

（掌聲）