Mathemagic

Can you mentally multiply enormous numbers faster than a calculator? Memorize a 100 digit number? Figure the day of the week of anyone’s birthday? These are just some of the many feats of mind that will be demonstrated at this event. Mathematics can be a difficult and perhaps puzzling subject for many. But watch in amazement as one of the world’s fastest human calculators shows his ability to turn math into magic. Arthur Benjamin, Ph.D. is a professor of Mathematics at Harvey Mudd College in Claremont, CA. He is the author of Secrets of Mental Math and Proofs that Really Count as well as co-editor of the journal Math Horizons. Fusing his love of both mathematics and magic, he has appeared at the World Science Festival in New York and the Magic Castle in Hollywood. Reader’s Digest calls him “America’s Best Math Whiz”.

46 thoughts on “Mathemagic

  1. Truly amazing. Seriously truly amazing.I would love to hear your opinion on how to solve our deficit. Your brilliance can be used many places.

  2. Mod 11 relies on the the place of the digits being used. The reason mod 9 is feasible even when the order is not known is because all powers of 10 are congruent to 1 in mod 9. The reason I believe that he relies on mod 9 is because I was thinking, how would he know if it was 9 or 0, and then later he seemed unsure about that case so it seemed like confirmation. It’s possible he used an alternative method though, but I don’t see how mod 11 helps, especially when divisibility by 11 isn’t known.

  3. Ok, now I see what you’re getting at.

    I’m not too familiar with mod 11, and I am unsure if you are too. Would it be possible of him to use this method to check whether it were a 0 or 9? I’m still positive he didn’t have problems with it. At best he was “buying” time to use an alternative method to check if it were a 0 or a 9.

  4. Ok then what if I chose to multiply by 2773. The numbers I would tell him are 2,1,7,1,2, and 5. 2+1+7+1+2+5=18, 1+8=9, then subtract 9 to get 0 according to you. But the last number would in fact be 9, since the number is 2171259.

  5. 10:14

    243567 = 2+4+3+5+6+7 = 27 which becomes 2+7 = 9. Subtract 9 from 9 is 0. I think you’re way over complicating things here…

    Since he is trying to “find” the number, he’d ALWAYS have to subtract from 9.

  6. Yeah but the problem with using that method is that if you have 9 and you subtract 9 you get zero so you can’t know if you need to subtract 9. He chose those last three digits so that the digit sum would be divisible by 9 because that number is already divisible by 9, but the problem is while he knows that the digit sum is divisible by 9, once you get to 9 you can still subtract 9 even though it’s already a single digit number. He makes up the story to probe him for information, in a fun way.

  7. All you have to do is continuously break down the numbers by addition until it reaches one digit, then subtract that from 9. Viola! That is your missing number.

    I seriously feel that he did not have trouble with it. It was purely showmanship. If he got everything right without some kind of element added, it’d be boring (a big wow the first time or two for the general populace, but that’s it)! Notice how he has to add “humor” throughout his entire talk?

  8. Actually there is no way he could distinguish between a 0 and a 9 because the digit sum of the number in mod 9 would be divisible by 9 regardless of whether is was 0 or 9.

  9. He didn’t have trouble with it; it was showmanship. It was something to keep the audience entertained and “captured”.

    For anyone curious, he used a checksum method.

  10. Sorry if I offended you or I came off as bragging. I was simply saying that, in my experience, technique is not required for dealing with numbers, or at least is has not been for me. It is a feat that I am proud of, but apologize if I came off as a know-it-all.

  11. Have not watched the video yet, but I have ~ 115 digits of pi memorized without any sort of technique, so I am interested in what it has to say.

  12. the reason they never taught you these methods is because math at school shouldnt be about the calculating itself but the understanding of mathematical thinking, so if they would teach you those methods they would also have to provide the evidence that these methods actually always work , which is much harder than the methods themself

  13. It’s because you usually have to have a firm understanding of mathematics (in particular arithmetic, and number theory) to do what he is doing. Calculators are quicker for laymen. A lot of common methods he may be using are special case methods, not generalized ones since there are many efficient ways of doing what he is likely employing as algorithms.

  14. Than it wouldn’t be a prime number. The only even number to be a prime number is two. All its multiples, by definition is not a prime number.

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