## Math Whiz Breaks Calculation Record 391

keyshawn632 writes

*"The Associated Press reports that Gert Mittring, 38, needed only 11.8 seconds to calculate the 13th root of a 100-digit number in his head at a math museum in Giessen, a small town, located in western Germany. It's worth noting though that his feat will not be recognized by The Guinness Book Of World Records because of the difficulty of standardizing such mathematical challenges."*
## What? (Score:5, Insightful)

## Re:What? (Score:5, Interesting)

memorizea 22 digit number in four seconds (according to the article) so I'm sure he can take a similar time to juggle the numbers around in his head. Perhaps his mental algorithm focuses on certain numbers at a time so that he can handle it.## Re:What? (Score:4, Informative)

Notice it took him 44.7 seconds to calculate the square root of a six digit number, but only 11.8 seconds to calculate the

13throot of a100digit number!!!!He also calculated the 23rd root of a 200 digit number in 40.83 seconds.

## Re:What? (Score:3, Interesting)

Show me any 13th power of an integer and I can immediately tell you the final digit of the root. Similarly with 5th powers and 9th powers. But square roots of non squares don't give so many tricks.

## Re:What? (Score:3, Interesting)

## Re:What? (Score:3, Insightful)

## Re:What? (Score:4, Informative)

## Re:What? (Score:5, Funny)

To memorize 22 digits, this guy takes ~4 seconds. So for 100 digits that would take about 18 seconds.

Now I forgot, he did what in 11.8 seconds

## Re:What? (Score:3, Funny)

## Re:What? (Score:3, Funny)

Having such a memory leads to other problems:

a) She will expect you to remember her birthday/holidays

b) She will know you will remember all the dumb things she said the last time you got in a fight

c) She will know you are smart enough to balance the checkbook (less money for her!)

My advice: Play dumb. It turns them on for some reason.

## Roomie in College (Score:5, Interesting)

In grade school he had memorized 52 decks of shuffled cards in some insane short period of time. The teacher would ask him what the 12th card of the 17 deck was... and he would start listing them forward and backward from there.

We often went to the casinos with him. He would card count and we just would bet whatever he would bet. We would all make a $100 or so and leave. He was always afraid of getting caught.

Some government agency approached him for running sets of numbers from point a to point b. They liked the fact that he could just put all those digits in his head without a papertrail.

Last I heard of him, he was avoiding math as much as possible... he enrolled in some DO program in a medical school somewhere. Numbers came too easy for this guy... and he knew he would go crazy if he went into a math field.

So now he's a doc somewhere. Probably calculating 10 by 10 digit numbers in his head as he examines you...

## Re:Roomie in College (Score:4, Insightful)

Memorizing and regurgitating and manipulating numbers is a very different skill from mathematics. These are things which computers are very good at - things which we DESIGN computers to be good at so we waste minimal time on such trivialities and work on the stuff which a computer can't do, the stuff which maths is really about: logical reasoning with abstracts.

My point is that just because he's good with numbers doesn't mean he'd enjoy (or be any good at) mathematics. Also, mathematicians can't count.

## I can do better (Score:3, Funny)

## Re:I can do better (Score:5, Funny)

"Name a state. Within a second, I'll tell you the capital of it.""Wisconsin""W."## Re:I can do better (Score:2)

I can confidently report that it is a Pödünk.

My wife reports that Giessen sports its own license plate code, to which I say: it's still a Pödünk.

## That's nothing (Score:3, Funny)

## Re:That's nothing (Score:2)

And a PC.

## 13 is an unlucky number!!!!! (Score:2, Funny)

OMG OMG OMG

## That's easy. (Score:5, Funny)

## Re:That's easy. (Score:5, Informative)

Just memorize the 13th root of every 100-digit number in existence. Sheesh.Let's just think about this for a minute.

100-digit numbers will fall between 10^99 and 10^100. Thirteenth-roots of such numbers will lie between 10^(99 / 13) and 10^(100 / 13), or in the range [41246264

But it's linear enough that the first nine digits of the 100-digit number yield a unique possibility for a root. And the last digit of the root will be the same as the last digit of the 100-digit number, because (N mod 10) always equals (N^13 mod 10). So the problem can be tackled from both ends, with the middle digits of the root being the hardest.

Of course, if the audience members are clued in, they can still beat the mental calculator hands down. Type the first nine digits, take the thirteenth root, and start reading off the digits; round up slightly to make the eighth significant digit match the final digit of the 100-digit number. Done.

A college professor of mine taught us how to square 3-digit numbers in our head in seconds using tricks like this; he was able to multiply arbitrary 5-digit numbers in his head, and often performed this onstage. And for the curious, yes, I do actually have a life outside slashdot.

## Re:That's easy. (Score:3, Informative)

## Re:That's easy. (Score:3, Informative)

if you're going to mention Professor Benjamin you mind as well use his name :)You beat me to it. (Retroactively.) Sorry Art.

P.S. Try solving one of these [olympicube.com] in eleven seconds.

## Re:That's easy. (Score:2)

It would be a better challenge if the computer came up with a random base (3 - 30, say), and a fairly random large number (that had an integral root in that base), and then they timed the guy over say 10 of these challenges.

## Re:That's easy. (Score:3, Interesting)

because (N mod 10) always equals (N^13 mod 10)I know I'm going to kick myself for asking this, but why is this necessarily true?

## Re:That's easy. (Score:5, Informative)

As for why it's true otherwise, it's because of Fermat's Little Theorem [wikipedia.org] and Euler's Totient Function [wikipedia.org]...

Specifically, since the Totient of 10 is 4, any number which is coprime to 10 (i.e. not even and not a multiple of 5) when raised to a power of 4, yields a 1 in the units place, (i.e. N^4 = 1 mod 10 if gcd(N,10) = 1).

Since if a number is coprime to 10, then all its powers are coprime to 10, N^12 = (N^3)^4 also has a 1 in its units place.

Now N^13 = N*(N^12) will always have the same last digit as N, if N is coprime to 10.

## Re:That's easy. (Score:5, Informative)

Since we use base 10 arithmetic (n mod 10) means we just look at the last digit. Digits repeat every fourth iteration when computing the powers of a natural number.

Numbers ending with:

1 -> 1,1,1,1,1,1,1,1,1,...

2 -> 2,4,8,6,2,4,8,6,2,...

3 -> 3,9,7,1,3,9,7,1,3,...

5 -> 5,5,5,5,5,5,5,5,5,...

You can see the period 4 cycles for 4, 6, 7, 8, and 9 as well. Since the digits repeat, the value of (n^k mod 10) must also repeat as k increases.

## I know you were joking, but... (Score:3, Insightful)

It's really interesting to think of all the hard limits in the universe caused by things like this.

## Re:That's easy. (Score:2)

Just memorize the 13th root of every 100-digit number. Sheesh.in existenceThanks for mentioning that, imagine the time I would have wasted had I tried to memorize all the 100-digit numbers that DONT'T exist. Thank you!

## Family guy (Score:4, Funny)

Lois: Peter, why would they make you presidesnt?

Peter: Maybe it's because I can recite all 50 states in a quarter of a second - RARF!

Lois: Peter, that was just a loud yelping noise

## Sources report... (Score:5, Funny)

## Re:Sources report... (Score:3, Funny)

RTFA

It says he's already got the 13th root, that's 12 more than required!

## And the answer is: (Score:3)

## Re:And the answer is: (Score:5, Funny)

## 38, ohhh (Score:2, Interesting)

## 11.8 Seconds (Score:2, Funny)

## Ironic...I'm currently listening to... (Score:5, Funny)

## I think I saw that guy... (Score:3, Funny)

## And still has 0.00005% of getting laid (Score:2)

## Re:And still has 0.00005% of getting laid (Score:2, Funny)

## Re:And still has 0.00005% of getting laid (Score:5, Funny)

And that would be the only rooting this guy will ever do in his life

## Guiness Book of World Records sucks anyhow... (Score:2)

## Devi: another brilliant mathematical mind (Score:5, Interesting)

The book itself was an interesting read, and at the time I just ate it up. It has a lot of tricks regarding number theory, mathematical riddles, calendar tricks, and calculation of pi, for example. It teaches how to figure the day of the week for any Gregorian date of any time in a few seconds, a trick which I still remember and use today!

As for the Pi, it contained a few poems and sayings whose letter counts signified the individual digits. I started trying to memorize pi, with my sights set firmly on the world record (as I am not without my own mathematical and mnemonic prowess). However, around grade 9, I decided to abandon my quest in order to get a life. I had memorized 1350 digits at that point.

One such quote held little significance for me at the time, but has since become hilarious. "How I want a drink, alcoholic of course, after the heavy chapters involving quantum mechanics!" Needless to say, my quantum prof found it quite funny. :)

## Re:Devi: another brilliant mathematical mind (Score:2)

Me too. Although I always forget what doomsday is this year (Sunday iirc).

## Re:Devi: another brilliant mathematical mind (Score:3, Interesting)

With some practice, you really can get to the point where you can calculate days of the week for any date in just a few seconds. People don't realize it's not all that difficult so it's a nice parlor trick.

Also included in that article are methods for remembering long-digit numbers, the order of a deck of cards, etc.

## Re:Devi: another brilliant mathematical mind (Score:2)

It teaches how to figure the day of the week for any Gregorian date of any time in a few seconds, a trick which I still remember and use today!Care to share? Sounds interesting!

## method to calculate the day of the week! (Score:5, Funny)

First, figure out the "year number". This part -- and the month number -- take some practice. Here's the first few to get you started:

1900 - 0

1904 - 5

1908 - 3

1912 - 1

1916 - 6

1920 - 4

1924 - 2

1928 - 0

And it repeats thusly. Note that the "year number" starts at 0 for the beginning of the century, and is decreased by two (modulo seven) every leap year.

In case you're interested in the other 75% of the time, simply add one to the year number for every year you add. Thus, 1901 becomes 1, 1902 becomes 2, etc.

The "month" number requires memorization of another table, which cannot be recalculated as quickly as the year number:

Jan - 0

Feb - 3

Mar - 3

Apr - 6

May - 1

Jun - 4

Jul - 6

Aug - 2

Sep - 5

Oct - 0

Nov - 3

Dec - 5

Add the month number to the year number. If your year is a leap year and your month is January or February, subtract 1.

Next, add the day number. The day number is the day. :P

Now, add or subtract sevens as necessary until you end up with a number between 0 and 6:

0 - Sunday

1 - Monday

2 - Tuesday

3 - Wednesday

4 - Thursday

5 - Friday

6 - Saturday

The result will be the day of the week.

If your desired date does not begin with a "19", you have to add a century number as well. I believe 2000 is a leap year, since every 100 years is not but every 400 years is. Thus, the century number of 2000 is 6 (or, equivalently, -1). 1800 is 5, 1700 is 3, etc. (I am not certain of these.)

As an example, today's year number is 5, the month number is 3, and the day number is 24. After compensating for the century by subtracting 1, we obtain 31. This reduces to 3 (by subtracting 28), which corresponds to Wednesday. Since it is Wednesday, and since I am in a large empty room, I further deduce that the lecture has ended.

## Re:method to calculate the day of the week! (Score:5, Funny)

Now where were we? Oh yeah - the important thing was I had an onion on my belt, which was the style at the time. They didn't have white onions because of the war. The only thing you could get was those big yellow ones...

## High pi (Score:5, Funny)

This isn't to say that 1350 digits wouldn't be useful! If you ever wake up in an alternate universe (you were warned about operating quantum machinery while drunk!) just look up pi in a math book. The degree of trouble you're in could correlate to the digit at which your memorized value, and the local value of pi, diverge.

If pi only diverges after 1000 or more digits, you're probably alright, except for having to re-memorize pi.

If pi diverges after 100 digits, there may be some minor historical divergences, like, say, President Nixon being impeached, or Bush winning a second term. The mind boggles!

If pi diverges after 30 or 40 digits, look out the window. Do dinosaurs roam the earth? Since you're surrounded by ruthless, math-book-publishing carnivores, consider donating yourself to the primate house of the zoo.

If local pi begins with a number other than 3, you should start to get worried, or maybe implode.

## Re:High pi (Score:2)

Imagine a (perfect) sphere the size of Earth, with a rope tight around some equatorial line, circumnavigating it. If you wanted to have the rope one meter above the ground all the way around the sphere, how much rope would you have to tie on to the end to do so?

The answer, as it's very easy to see after knowing the answer, is 2Pi meters, or about 6.28 meters. Most people, without checking the

## Repost? (Score:2)

## Uh oh (Score:5, Funny)

## Re:High pi (Score:5, Interesting)

I read somewhere that you only need about 50 digits of pi to describe a circle the size of the observable universe to within the diameter of a proton, let alone a chocolate donut.Well, let us see:

radius universe: about 15e9 lightyears

radius proton: 1.2e-15 m

circle with the size of the universe divided by diameter proton:

2*pi*15e9*365*24*3600*300000000/(2*1.2e-

So 42 digits of pi will do.

42? Where did I see this number before?

Nyh

## My Turn (Score:2, Funny)

2 One Thousand

3 One Thousand

4 One Thousand

5 One Thousand

6 One Thousand

7 One Thousand

8 One Thousand

9 One Thousand

10 One Thousand

11 One Thousand

12 One Thousand

FVCK!#$

## The first mentat? (Score:5, Funny)

## Re:The first mentat? (Score:2)

It is by the juice of caffiene that thoughts aquires speed, the hands develop shakes, the shakes become a warning.

It is by will alone I set my code in motion.

--Coder's litany.## I so call bullshit (Score:5, Interesting)

There has to be a trick to it aside from "thinking really fast"

Tom

## Re:I so call bullshit (Score:5, Insightful)

There has to be a trick to it aside from "thinking really fast"Well of course, there is. Probably two or three tricks combined. .

plusthinking really fast, as well as having a good memory for numbers.Walking a tightrope is more than just having "good balance," and it's really just a trick, and not necessarily a very useful one, but. .

It

isstill pretty impressive and you can't do it.KFG

## ahh (Score:5, Funny)

It's worth noting though that his feat will not be recognized by The Guinness Book Of World Records because of the difficulty of standardizing such mathematical challenges.That's the problem when dealing with a highly subjective field like mathematics.

## What he will be doing next week... (Score:5, Insightful)

Probably breaking codes for some government or another. Someone with talent with numbers and such will catch the eye of someone out there. Could it be that this was just to show off his talent as a sort of "job interview"? Probably not, but I expect he will get some calls about it anyway.

## The future is here (Score:4, Interesting)

I would like to know how much of this ability is genetically determined and how much is due to training and from what age did his "gifts" become apparent.

Either he needs to be stuck into some kinda breeding program (perhaps solving his virginity problem *hyuk hyuk*) or his training regimen needs to be studied and duplicated en masse. Imagine an advanced state-of-the-art military computer system that runs on 3-square meals a day and isn't susceptible to EMP bursts.

## dumb tricks... (Score:2, Interesting)

The implicaton is this guy is a genius. Maybe he is, but calculating roots quickly doesn't make you a genius, it just means you know some math tricks. Isn't this just the mathematical equivalent of

## Re:dumb tricks... (Score:2)

## Re:dumb tricks... (Score:2)

## Re:dumb tricks... (Score:2)

I don't think you've thought very much about "useful" or "genius".

I think I know what the word genius is intended to mean, especially since I'm the one using the word. You can quote however many dictionary definitions you like, but that doesn't change the fact that most useage of the word genius is using definition 5. Here's the 10 definitions of the word dog for instance:

1 a : CANID; especially : a highly variable domestic mammal (Canis familiaris) closely related to the common wolf (Canis lupus) b

## Gert disqualified and sued! (Score:5, Funny)

The news set off a legal feeding frenzy. SCO sued Mr. Mittring for using the company's super secret 13th root finder source code. Microsoft then added to the man's woes by suing for patent infringement over Microsoft's patents on 100 digit numbers. RIAA then sued him for including "8675309" in the answer -- obviously a stolen clip from "Jenny" by Tommy Tutone.

## Photo of Gert Mittring here (Score:4, Informative)

Please note his rather tasteful attire.

The page also has information on the actual rules on calculating the 13th root of a 100 digit number.

## 11.8 seconds? (Score:2, Funny)

## Increasing math ability (Score:3, Interesting)

I always wonder if there is a condition that works in the opposite way, a bit like dyslexia for reading/writing for maths, a sort of "mathlexia" if you will. Just as dyslexia doesn't mean you're stupid, it's just that your particular model of brain doesn't comprehend words straight away, a person with "mathlexia" can't add up 137 and 48 in their head to save their life, let alone do anything complicated like division or factorisation.

If there is such a thing as mathlexia, I'd say I've definately got it. The funny thing is, I love computers, I love programming (in C among other languages, though a mastering of assembly has persistently eluded my efforts), and I can understand even engineering diagrams and other geeky stuff. I kicked ass in English Literature at high school (even though I didn't particularly enjoy it and it's not where my passions lie); but I cannot do maths in my head if my life depended on it. Even with a calculator I get lost in the process of doing a complicated sum, but I would say I'm at least a half decent programmer. It's not that I have a problem with a logical process, it's the math part that throws me.

Is it just the way my brain is wired? Is there a big secret no-one's telling me that will make this all easy? Am I destined for a life of going "uh huh? righto..." when someone explains a (pure) math concept to me? Or is there some hope for a math dummy like me?

If anyone knows the answer(s) to any of this I would be eternally thankful.

## Re:Increasing math ability (Score:2)

There is a simple trick to math, that sounds bleeding obvious, but it took me years to truly figure out- once I did, it all became really easy.

Math is really easy. Just learn the process, apply it, and you will always get the right answer. You say you have no problem with the logical processes- well thats all math is.

The big secret is that there isn't a big secret. Unless you've forgotten your addition and multiplication tables,

## Re:Increasing math ability (Score:2)

In any case, going through the process is really easy to screw up unless you understand the underlying concept. That understanding (like what exactly does an integral

mean?) is what can be hard for some people.## Re:Increasing math ability (Score:2)

999+999... 18, 198, 1998 done.It's easier for me to do that as 1000+999-1=1999-1=1998.

Just another way to look at it.

## Here's a challenge (Score:2)

Fastest time to find the char-2 differential profile of a random bijective 4x4 look up table. No gimmicky tricks there just pure nlogn work in your head

From what others have posted and I've read on the net the 13th root is a trick to a large part. The leading digits are a strong indicator of the value of the root, etc, etc, etc.

Or something with more practical implications... fastest time to perform an inverse cosine transform [type used in MPEG video] of an 8x8 matrix i

## To put it into perspective (Score:2, Informative)

## Oh come on now. (Score:5, Funny)

I can do the 23rd root of a 163 digit number in 5.8 seconds, and I wasn't even trying. I've climbed Mt. Everest in an hour and a half. I can rewrite the Linux kernel in under an hour. I can count up to ten thousand coins in no more than a minute.

And yet, curiously, it takes me almost...-checks watch- five minutes to make a stupid, useless post on /. Strange eh?

## If I recall... (Score:4, Interesting)

## To how many significant figures? (Score:5, Interesting)

The 13th root of a 100-digit number will always have 7 digits. If you memorize the first few digits of the 13th powers of numbers between 49 and 58 and you are given a 100-digit number, then you immediately know the first 2 digits of the 13th root. Memorize the initial digits of 13th power of numbers between 491 and 588 and you immediately know the first 3 digits. By memorizing the terminal digits of 13th powers of numbers less than 100, you could similarly immediately get the last 3 digits. That leaves 1 digit to compute, which is a slightly less impressive-sounding feat for 11.8 seconds. It's not a trivial calculation, though, and not at all shabby for 11.8 seconds.

Jonathan

## silly question begging to be asked (Score:2, Funny)

at a math museum in Giessena

math??? can someone explain what a math museum contains? surely not the pickled brain of Leibnitz next to Pascal's toothbrush?museum## Rapid math tips and tricks by Edward Julius (Score:3, Informative)

Cheap new. Even cheaper used (check Amazon).

The book is thin and has a white cover with blue and red lettering.

## This is not as difficult as it sounds. (Score:5, Informative)

1. The leading digit is ALWAYS 4.

2. The last digit of the 13-th root of N is always the same as the last digit of N.

(The first fact follows because Floor[N[(10^100 - 1)^(1/13)]] = 49238826 and Floor[N[(10^99 - 1)^(1/13)]] = 41246263. The second holds because N^13 is congruent to N modulo 10.)

With minimal practice, you can get the second-highest digit from the magnitude. Beyond that I can only speculate what he's doing. But by taking an alternating sum of the digits, you get its value mod 11, which gives you the value of the root mod 11, which buys you another digit. Now you're halfway there...

## Re:This is not as difficult as it sounds. (Score:5, Funny)

Of course, to be fair, it should be noted that the above poster is a postdoc lecturer at MIT who is teaching Mathematics for Computer Science this semester and wrote the course notes, including a substantial portion involving number theory.

Oh God, now that I think about it . . . you're putting this on the final, aren't you? NOoOOOooOooOoOOoO!!!!!

## Some of the methods used (Score:5, Informative)

http://racine13eme.site.voila.fr/100digang.htm [voila.fr]

-pvg

## Met him last week! (Score:3, Interesting)

He has an interesting way of getting along financially. Basically, he's living off an exclusive contract with the German TV station RTL [www.rtl.de] where he's featured every now and then in shows. He also gives lectures on mathematical topics; RTL makes him charge a very steep EUR 2500 per lecture (about $3000). I think originally he studied psychology; he's still running the psychiatrist's practice in Cologne that he startet off with.

We were joking about him tackling the Millenium Problems now; I wonder if he's serious about that... but then, there's more to it than calculating in your head really fast.

## Re:Hrmm (Score:2, Insightful)

## Re:Hrmm (Score:3, Funny)

## Quick! (Score:3, Funny)

## Re:Quick! (Score:3, Funny)

Cheers,

Adolfo

## Re:Quick! (Score:3, Funny)

## Re:I can (seriously) do 43rd root of 100 digit num (Score:2, Informative)

## Re:I can (seriously) do 43rd root of 100 digit num (Score:3, Funny)

Dont believe me?

I dont believe you either.

So stop bullshitting.

## Re:I can (seriously) do 43rd root of 100 digit num (Score:3, Informative)

There are only about dozen perfect 43rd powers with exactly 100 digits. You only need to memorize the first

2 digitsof those perfect powers to be able to spit out the right root instantly.-

## Re:I can (seriously) do 43rd root of 100 digit num (Score:5, Informative)

Well, I guess that's not so outrageous depending on the precision you need. All the 43rd roots of 100 digit numbers are greater than 200 and less than 212, so if you only need integer precision you only have 13 choices. And memorizing 12 thresholds is not

thathard.## Re:Yes, But... (Score:2)

## Re:Yes, But... (Score:2)

## Re:Yes, But... (Score:2)

## Re:Although (Score:3, Funny)

1 + 1 = 10

## Re:This is very nearly as important (Score:4, Funny)

## Re:This is very nearly as important (Score:2)

## Re:Bounds (Score:2, Informative)

Someone already mentioned his memorization skills. I think this was the trick. Someone memorized tons and tons of digits of pi. So when someone starts reading a random section of digits he can recite the next hundred or so. Doesn't mean he calculates pi every time.

## Simpler than that (Score:5, Informative)

That leaves you with a mere... 7,193,306 possible roots to memorize.

I don't know how they do it, but I am familiar with modulo-10 math "tricks". For example, did you know that if you add up the individial digits in any number and the result is divisible by 3, then the original number is divisible by 3? For example "621". 6+2+1=9, and so 621 is divisible by 3 (Try it: 621/3=207).

13th root has similar magic: the 13th root of any number will have the same last digit as the number you are trying to take the root of. For example, the 13th root of 2235879388560037062539773567 is 127. Notice that they both end in 7. An integer and its 13th power always ends in the same digit. Try it.

The point is, that little trick itself reduces the problem space by a factor of 10 right there. So I'm assuming they've studied and learned further tricks like these. Ask them for the 11th root of the same number and they'll probably come up completely blank.

## Re:"memorizing 22 random digits in just four secon (Score:2, Interesting)