Faster than a Calculator by Arthur Benjamin at TEDxOxford (Transcript)

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.

24. 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?

[Audience: 576].

576 is 331776.

Yes? Good. How about another three-digit number, sir? Three digit number?

[Audience: 103.]

103 is 10609, too easy. Another three-digit number, please?

[Audience: 125].

125 is 15625 but that’s 5 to 6 power, so that was easy too. How about another three digit number sir?

[Audience: 985]

985 is 970225, yes, thumbs up, if it’s right. One more three digit number sir?

[Audience: 926]

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?

[Audience: Yes]

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.

[Audience: 1992]

1992, and the month? July what? 3rd — was that a Friday?

[Audience: Yes.]

Yes, excellent. Somebody else? Yes sir, green shirt, what year?

[Audience: 1992]

1992 and the month? June what? 30^th? Was that a Tuesday? Excellent. Somebody else, how about you, what year? I am sorry so what year was it?

[Audience: 1995]

1995 and what month? June what? 26? Was that a Monday? Excellent. And I see a hand up in the balcony. Young lady. Let me try something different here. Your birth day, what – what year was it – what day of the week was it, tell me in advance the day of the week?

[Audience: Thursday]

Thursday and what year was it? 2002. Did it happen to be on? May 2^nd.

[Audience: Yes]

That’s my daughter, I knew that one. I was there on that Thursday.

Anybody do we have anybody here who does not know the day of the week they were born but would like to find out? Okay, now let’s see. Now of course if you don’t know what it is, I could just make up and answer and you’d probably believe me, but I don’t want you to have to do that. So I come prepared for that situation. There is an app for everything these days. So I will ask one of you here just to take this and so give us your year and then type in the year right in that, what year? 1995. So type in 1995, great. And what month? September, press the September button there and that should give you a calendar – September what? 21^st I believe was a Thursday, can we get confirmation? It was Thursday, good.

I’ll tell you what, you know since you have the app with you, let’s try something trickier. The app actually goes as far into the future as 3,000 as far back into the past as 1600. Don’t go below 1600 because then we get off the Gregorian calendar and that messes me up a little. So what year would you like, choose a year between 1600 and 3000? Go ahead.

[Audience: 2730]

2730, so enter 2,730 into that and what month would you like, June, what 13. Will that be a Friday? Yes and it’ll be cloudy on that day too, if I am not mistaken. Thank you very much.

In fact, anybody else who wants to find out their birthday, see me in the lobby perhaps in the break or so. I’ll be more than happy to tell you. Now I have just a little bit of time left, so I’d like to do one last thing for you that I alluded to earlier when we had the other calculators on stage. I’m going to try to square a five digit number requiring if you have it a 10 digit calculator or higher, feel free to bring out your calculator at this point. But to make my job more interesting for you 4as well as for me I’m going to do this last problem thinking out loud, so you can actually honestly hear what’s going on in my mind while I do a calculation of this size. Let’s create a five digit number, how about we go – we just go up with this aisle, the first five people along the aisle, each give me a single digit that will be my five digit number?

3, 7, 6, 9, 1.

37,691 squared. Let me explain to you how I’m going to attempt this problem. I am going to break the problem down into three parts. I will do 37,000 squared plus 691 squared plus 37,000 times 691 times 2. Add all those numbers together and with any luck arrive at the answer.

Now let me explain one more thing. While I do this calculation, you might hear certain words as opposed to numbers creep into the calculation. Let me explain what that is. This is a phonetic code, a mnemonic device that I use that allows me to convert numbers into words. I store them as words and later on retrieve them as numbers. I know it sounds complicated, it’s not. I just don’t want you to think you’re seeing something out of rainman here. There’s definitely a method to my madness definitely, definitely.

One last instruction for my judges with calculators, now who’s got an answer in front of them. Raise your hand, okay enough of you. There is a 50% chance that I will make a mistake on this problem. If I do, don’t tell me what the mistake is, just say you’re close or something and I’ll try and figure it out which can be pretty entertaining in itself. If however I am right, whatever you do don’t keep it to yourself, make sure everybody knows that I got the answer right because this is my big finish.

Okay, so without any more stalling, here we go. I will start the problem in the middle with 37 times 691, now let’s see oh my gosh, there’s that 700 minus 9, I will take advantage of that, and 700 times 37 is 25,900; 37 times 9 is 333, subtract the two, to get 25,567, double that to get 51,134. Okay, 51000 becomes light tomorrow, is 51134, that seems right, I will go on.

Next I do 37 squared which is 1369 so I can say 1 billion, take the 369 and that too light, is there going to be carrying, 369 and that’s like to get 420 million tomorrow tomorrow okay, yes, we do 691 squared, that 700 times 682 plus nine squared, that’s 477,481, raft if I need a raft take the 477 and that to tomorrow to get 611,481.

Yes, good. Thank you all very much. I hope you enjoyed mathemagics. I am Arthur Benjamin.

Thank you.

 

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