Transcript of Faster than a Calculator by Arthur Benjamin at TEDxOxford
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Arthur Benjamin – Mathemagician
Well good afternoon, ladies and gentlemen. My name is Art Benjamin, and I am a mathemagician. What that means is, I combine my loves of math, or I should say maths and magic to do what I call “mathemagics.”
But before I get started, I’ve got a quick question for the audience. By any chance, did anyone – anyone here in the audience happen to bring with them this afternoon a calculator? If you have one, perhaps on your phone or somewhere and you are pretty comfortable using it, raise your hand. I will need a couple of people to help me out here. I see one, two and perhaps one more. Three, the three of you bring out your calculators and join me up here on stage and let’s give these volunteers a nice round of applause. Come on up!
Great. Over on this side please. Awesome. Now, since I have not 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?
Oh, that’s fine. 74. And another – how about another two-digit number, how about on this side?
Multiply 74 times 39 on the calculator, make sure you get 2886, or the calculators are not working. Do each of you get 2886? Give them a round of applause.
Now I notice it took some of us a little bit of time to get the answer. That’s okay. 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? 25. Six squared would be 36. 73 squared would be something else, yeah.
Now on most of these calculators they have little shortcut buttons that allow you to square numbers even faster. What I’m going to try and do now is to square, and you might test and make sure you could square 5 or 6 with it but what I am going to try and do is to square in my head, three two-digit numbers faster than they can do on their calculators, even using the shortcut method. What I’ll ask is three people, how about in the third row here, one, two, three, each yell out a two digit number and if you would square the first one, the second and third one, I will try and race you to the answer. So quickly, a two-digit number please.
- Great, next. 98, and one more, 26. Would you call out your answers, please?
[Audience: 576, 9604, 676.]
Give them a round of 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 at all, call out a three-digit number. Anyone on our panel, verify the answer. Now if I get the answer right, give me a big thumbs up, if I make a mistake, let me know and I will try and fix it. A three-digit number, anyone?
576 is 331776.
Yes? Good. How about another three-digit number, sir? Three digit number?
103 is 10609, too easy. Another three-digit number, please?
125 is 15625 but that’s 5 to 6 power, so that was easy too. How about another three digit number sir?
985 is 970225, yes, thumbs up, if it’s right. One more three digit number sir?
Oh, 926 is 857476.
Thank you very much.
Let me try to take this one step further. I’m going to try to square a four-digit number this time. I am not going to beat you to the answer on this one, but I will try to get the answer right. To make this a little bit more random, how about we use the fourth row four people, each of you call out a single digit between zero and nine, that will be the four-digit number that I’ll square.
1, 5, 7, 7
1577, this will take me a little bit of time, so bear with me. 3,486929.. no, don’t tell me. Number was 1577. Oh, wait, wait, 2,486929. [Was everything else right? Thank you very much. What’s one million off, that’s all I ask.
Now, I would attempt to square a five-digit number — and I can — but unfortunately, most calculators cannot.
So since we’ve reached the limits of our calculators – although some of yours may go higher, I am going to try to conclude the first part of my show by trying something even trickier. Let’s take the first number on the board here, 576. Would you each enter 576 on your calculator? And instead of squaring it this time, I’d like you to take that number and multiply it by any four digit number that you want, but don’t make it too easy like 1000 or 1234, but some random four digit number. So you should have as an answer either a six-digit or possibly a seven-digit number. How many digits are you in your answers, six or seven digits?
Seven, seven, six.
Is there any possible way that I could know what six or seven-digit numbers they have? Say “No.” Good, then I shall attempt the impossible — or at least the improbable. What I’d like each of you to do is to call out for me any six of your seven digits, so in your case, five of your six digits in any order you’d like. One digit at a time, I shall try and determine the digit you’ve left out. So starting with your six digit number, call out any five of them please.
[Audience: 8, 0, 9, 3, 8. ]
Did you leave out the number 8?
[Audience: Yes, I did.]
Yes, that’s one. You have got a seven-digit number, call any six of yours loud and clear.
[Audience: 4, 7, 2, 5, 8.]
Did you leave out the number 6?
That’s too. The odds of me getting all three of these right by pure guessing would be one in 1000, 10 to the third power.
Okay. Any six of your digits, really scramble them up this time.
[Audience: 9, 4, 4, 5, 4, 4]
Did you also leave out the number 6?
Great and let’s give all three of these people a nice round of applause. Thank you very much.
For my next number — I have another question for the audience. By any chance, does anybody here happen to know the day of the week that they were born on? If you think you know your actual birth day, raise your hand. Starting with you, what year if I may.
1992, and the month? July what? 3rd — was that a Friday?
Yes, excellent. Somebody else? Yes sir, green shirt, what year?