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Well, good morning ladies and gentlemen. My name is Art Benjamin, and I am a "mathemagician." What that means is, I combine my loves of math and magic to do something I call "mathemagics." But before I get started, I have a quick question for the audience. By any chance, did anyone happen to bring with them this morning a calculator? Seriously, if you have a calculator with you, raise your hand, raise your hand.

I — was — your hand go up? Now bring it out, bring it out. Anybody else? I see, I see one way in the back. You sir, that's three, And anybody on this side here? OK, you over there on the aisle. Would the four of you with calculators please bring out your calculators, then join me up on stage. And let's give these volunteers a nice round of applause.

(Applause)

That's right. Now, since I haven't had the chance to work with these calculators, I need to make sure that they are all working properly. Would somebody get us started by giving us a two-digit number please? How about a two-digit number?

Audience: 22.

Arthur Benjamin: 22. And another two-digit number, Sir?

Audience: 47.

AB: Multiply 22 times 47, make sure you get 1,034, or the calculators are not working. Do all of you get 1,034? 1,034?

Woman: No.

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

(Applause)

Would you like to try a more standard calculator, just in case? OK, great. What I'm going to try and do then — I notice that took some of you a little bit of time to get your answer. That's OK. I'll give you a shortcut for multiplying even faster on the calculator. There is something called the square of a number, which most of you know is taking a number and multiplying it by itself. For instance, five squared would be?

Audience: 25.

AB: 25. Now, the way we can square on most calculators — let me demonstrate with this one — is by taking the number, such as five, hitting "times" and then "equals," and on most calculators that will give you the square. On some of these ancient RPN calculators, you've got an "x squared" button on it, will allow you to do the calculation even faster. What I'm going to try and do now is to square, in my head, four two-digit numbers faster than they can do on their calculators, even using the shortcut method. What I'll use is the second row this time, and I'll get four of you — one, two, three, four — to each yell out a two-digit number, and if you would square the first number, and if you would square the second, the third and the fourth, I will try and race you to the answer. OK? So quickly, a two-digit number please.

Audience: 37.

AB: 37 squared, OK.

Audience: 23.

AB: 23 squared, OK.

Audience: 59.

AB: 59 squared, OK, and finally?

Audience: 93.

AB: 93 squared. Would you call out your answers, please?

Woman: 1369. AB: 1369.

Woman: 529.

AB: 529.

Man: 3481.

AB: 3481.

Man: 8649.

AB: Thank you very much.

(Applause)

Let me try to take this one step further. I'm going to try to square some three-digit numbers this time. I won't even write these down — I'll just call them out as they're called out to me. Anyone I point to, call out a three-digit number. Anyone on our panel, verify the answer. Just give some indication if it's right. A three-digit number, sir, yes?

Audience: 987.

AB: 987 squared is 974,169.

(Laughter)

Yes? Good. Another, another three-digit — (Applause) — another three-digit number, sir?

Audience: 457.

I — was — your hand go up? Now bring it out, bring it out. Anybody else? I see, I see one way in the back. You sir, that's three, And anybody on this side here? OK, you over there on the aisle. Would the four of you with calculators please bring out your calculators, then join me up on stage. And let's give these volunteers a nice round of applause.

(Applause)

That's right. Now, since I haven't had the chance to work with these calculators, I need to make sure that they are all working properly. Would somebody get us started by giving us a two-digit number please? How about a two-digit number?

Audience: 22.

Arthur Benjamin: 22. And another two-digit number, Sir?

Audience: 47.

AB: Multiply 22 times 47, make sure you get 1,034, or the calculators are not working. Do all of you get 1,034? 1,034?

Woman: No.

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

(Applause)

Would you like to try a more standard calculator, just in case? OK, great. What I'm going to try and do then — I notice that took some of you a little bit of time to get your answer. That's OK. I'll give you a shortcut for multiplying even faster on the calculator. There is something called the square of a number, which most of you know is taking a number and multiplying it by itself. For instance, five squared would be?

Audience: 25.

AB: 25. Now, the way we can square on most calculators — let me demonstrate with this one — is by taking the number, such as five, hitting "times" and then "equals," and on most calculators that will give you the square. On some of these ancient RPN calculators, you've got an "x squared" button on it, will allow you to do the calculation even faster. What I'm going to try and do now is to square, in my head, four two-digit numbers faster than they can do on their calculators, even using the shortcut method. What I'll use is the second row this time, and I'll get four of you — one, two, three, four — to each yell out a two-digit number, and if you would square the first number, and if you would square the second, the third and the fourth, I will try and race you to the answer. OK? So quickly, a two-digit number please.

Audience: 37.

AB: 37 squared, OK.

Audience: 23.

AB: 23 squared, OK.

Audience: 59.

AB: 59 squared, OK, and finally?

Audience: 93.

AB: 93 squared. Would you call out your answers, please?

Woman: 1369. AB: 1369.

Woman: 529.

AB: 529.

Man: 3481.

AB: 3481.

Man: 8649.

AB: Thank you very much.

(Applause)

Let me try to take this one step further. I'm going to try to square some three-digit numbers this time. I won't even write these down — I'll just call them out as they're called out to me. Anyone I point to, call out a three-digit number. Anyone on our panel, verify the answer. Just give some indication if it's right. A three-digit number, sir, yes?

Audience: 987.

AB: 987 squared is 974,169.

(Laughter)

Yes? Good. Another, another three-digit — (Applause) — another three-digit number, sir?

Audience: 457.

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