Unlocking the Magic of Math

On the Imagine Solutions stage, Arthur Benjamin demonstrates his incredible ability to accurately calculate complex mathematical functions in his head in astonishingly short time. A math professor by day, Arthur travels all around the world giving audiences a view inside the mind of a mathemagician. You’ll be amazed by his intellectual pyrotechnics, and entertained by his high-energy, humor-infused, interactive style, engaging the audience as he produces calculations most of us couldn’t even fathom doing without a trusted calculator. Watch, learn, laugh a little, but mostly be amazed.

we do a wonderful job today thank you well good afternoon ladies and gentlemen my name is art Benjamin and I am a Mathemagician what that means as I combine my loves of math and magic to do something I call mathematics but before I go any further I've got a quick question for the audience by any chance did anyone happen to bring with them this afternoon a calculator if you happen to have one perhaps on your phone and if you're comfortable using it raise your hand I need a few people to help me out with their calculators I see one person there one and they go to and perhaps one more three with the three of you bring out your calculators join me up here on stage and let's give these volunteers a nice round of applause thank you very much thank you for that
all right there will be great yeah cut right up on stage one more round of applause for our brave volunteers thank you right this way and I'm not going to do anything hard now since I have not had a chance to work with your calculators I need to furrow we got four people even better since I haven't had a chance to work with their calculators I need to make sure they are all working properly would somebody get us started by giving us a two digit number sir how about a two digit number 26 and another two digit number please 34 multiply 26 times 34 make sure you get 884 exactly or the calculators are not working you get 884 884 making a phone call there 884 let's give them a round of applause that's got to unlock the calculator there fantastic now I notice that took some of us a little time to get the answer and that's okay
I'll give you a shortcut for multiplying even faster there's 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 bigger right now most of these calculators actually have little shortcuts for squaring and if you know them you should use them like on this one if you want a square five you press five then times and then equals and that will give you the square some of yours have a little x squared buttons that'll do it even faster what I'm going to try and do now is to square in my head for two-digit numbers faster than they can do on their calculators even using the shortcut method well last is for people how about here in the first row one two three four each yell out a two-digit number and if you would square the first number the second the third and the fourth one I
will try and race you to the answer so quickly a two-digit number please 32 squared okay next 81 squared next what is that 13 squared and one more 46 would you call out your answers please 1024 6560 1 1 6 9 and finally give them a round of applause thank you 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 anyone at all call out a three-digit number anyone on our panel verify the answer if I get the answer right give me a thumbs up or show everyone the answer if I make a mistake let me know and I'll try and fix it a three-digit number anyone what was that
again 227 squared is 50 1529 5 1 5 2 9 great another three-digit number please three-digit number 355 is 120 6025 one two six zero two five great another three-digit number or sir 999 is 998 thousand and 1 9 9 8 0 0 how about one more three-digit number go ahead well 104 seven four eight is oh that's a hard one five hundred fifty nine thousand five hundred and four thank you very much [Applause] let me try to take this one step further I'm going to try to square a four-digit number this time now I'm not going to beat you to the answer on this one I promise but I will try to get the answer right to make this a little bit more random how about we use four people in the second row this time one two three
four each call out a single digit that will be the four digit number that I'll use eight nine what was that five seven eight nine five seven this will take me a little bit of time woah so bear with me eighty million two hundred twenty seven thousand eight hundred forty nine good thank you very much now I would attempt to square a five digit number and I can but unfortunately some calculators don't go that high wouldn't want to embarrass them although I think most of yours do and I will talk to you about that later but in the meanwhile let me conclude the first part of my show by trying something even trickier let's take the first big number on the board here six
five six one would you each answer six five six one on your calculator and instead of squaring at this time I'd like you to take that number and multiply it by any three-digit number that you'd like but don't tell me what you're multiplying by just multiply it by any random three-digit number so you should have as an answer either a six digit or probably a seven digit number do each of you have a seven digit number by chance seven digit seven six digits and seven I think is there any possible way that I could know what six or seven digit numbers they have say no good then I shall attempt Ted day you're still working on your account you're giving me a little concern there you have a seven did you answer at this point six digits well then you've made a mistake okay start again take six five six one times any three-digit number
okay what I'm going to ask each of them to do is to call out for me any six of their seven digits or and Ted you have seven digits now and or a bill your case call out 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 seven digit number call out any six of them please I'll repeat them so the audience can hear eight eight four zero two seven did you leave out the number seven good good that's one you've got a seven digit number called any six of yours loud and clear zero four five did you say four zero four five four zero five oh I'm
having a little trouble with this one I don't forget your number I'll get back to you you bill you've got a six digit number called five of your six in any order three six one two seven I believe you left out the number eight great Ted you the odds of me getting all four of these by pure guessing would be 1 in 10,000 Ted Quad six a year seven in any order five six three one three three did you leave out the number six good I was worried about that one Tony I've got one troublemaker left here at San tatts you do me a favor if you would concentrate on the digit you left out it doesn't do any good I know it just looks dramatic here and yet I seem to be getting a lot of nothing you didn't leave out a zero did you know because it
seemed like you're thinking of nothing all right concentrate hard I'm going to get at this time you left out the number nine exactly and let's give all four of these people a nice round of applause thank you very much well done for my next number most audiences don't get that I've got another question for the audience by any chance does anyone here happen to know the day of the week that they were actually born on if you think you know your actual birthday and you're willing to share it raise your hand okay sorry you sir what year if I may what year was it 1939 and what month may what 12th was that a Friday yes good somebody else who else yes please shout
it out what year 56 and 36 okay and the month August what was that 25th was that a Tuesday excellent somebody else one more person here yes sir what year 47 in the month February what 26 was that a Wednesday yes anyone here who does not know their day of week but always wanted to find out James okay you got your hand up right away I'll let you be now tell you now of course if you don't know what it is I could you know just make up an answer and you'd probably believe me but luckily as as Tyler said there are apps for everything these days how I'll ask you to help me out once again all you have to do is scroll to the right year and and the rest is pretty simple so James what year if I may
I go back to 1932 okay let me think about that for July 26th I believe is a Tuesday let's see if the app agrees with me thank you I tell you what highlight as long as you have the app with you let's try something even trickier the app will go as far into the past as 1600 and as far into the future as the year 10,000 oh do i do hila do you want to go into the past or into the future into the future of course that's what this conference is all about all right well how to scroll as far as you'd like all the way you know don't go past 10,000 the Apple and lets you do that and when you find a year that you're happy with let me know what year would you like like to do oh you got it got a particular year in mind I can tell
all right what year would you like [Music] 4304 okay let me think about that alright and a month Beth give us a month please August August what 12th will that be a Friday yes and it'll be cloudy I think thank you very much thank you by the way if anyone else wants to find out their day of the week see me after the show I will be hanging out at my table in that corner Randy actually gave me a table to hang out on after the show I'll be more than happy to tell you well folks the last thing I'm going to do for you today because as a professor of mathematics I and I am my full-time job as professor of mathematics at Harvey Mudd College in
Claremont California and and I wouldn't be doing my job today if I didn't give you a little bit of a sense as to what's actually going on in my head now if you want all the details I have some books and DVDs that Randy said I could offer at my table I'll have them in the back corner see me after the show if you're interested but I'm gonna sraight now not so much explain but let you enter my mind so you can hear what actually is going in my head while I do a giant calculation let's create this time a five digit number something I mentioned that I would try earlier but to make my job more interesting for you as well as for me I will do this problem thinking out loud let's get the third row this time I get a fee of five people each call out a single digit that will be my five digit number seven three eight four
six oh boy this is not gonna be an easy one seventy-three thousand eight hundred forty six squared yuck let me explain to you how I'm going to attempt this problem I'm going to break the problem down into three parts I'll do 73,000 squared plus 846 squared plus 73 thousand times 846 times two that's the hard part add all those numbers together and with any luck arrive at the answer now let me recap thank you while I explain something else as I do this last calculation you will hear certain words not just numbers but actual words enter the calculation let me explain what that is this is a
phonetic code that I use that allows me to convert numbers into words I store them as words 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 Rain Man here there's definitely a method to my madness one last instruction for my judges with calculators now who's got an answer raise their hand a few of you good you should have a ten digit number beginning with five ending with six in between I don't know yet there's a 50% chance that I'll make a mistake somewhere in the middle 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 yourselves 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'll start the problem the middle
with 73 times eight 46 73 times eight 46 how am I going to do that I'll take 73 times 84 first 73 times 84 is 84 is seven times twelve 73 times seven is five hundred eleven times twelve is six thousand one hundred thirty-two that's us sixty one thousand three hundred twenty plus four thirty-eight is 60 1758 60 1758 double that to get 120 3516 120 3516 that seems right I'm checking I'm checking seems right I'll go on 123 516 becomes denim denim loaded Devon denim loaded or lettuce is a 1 2 3 5 16 haven't said any part of my answer but I'm about to denim loaded okay finally we do 73 squared which is 5 3 2 9 so I can say five billion take the three 29 add that to denim 329 I see a carry coming so I'm gonna say 330 and
that to 123 to get 453 million let it's lettuce xocai finally we do 846 squared that's 800 times 892 plus 46 squared that's 714 thousand six hundred plus 2116 the seven hundred fifteen thousand seven sixteen cottage if I need a cottage take the 715 add that to let it to get 230 1716 yes good thank you all very much I hope you enjoyed mathemagics I'm Arthur Benjamin thank you

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