Computing 13th root from a hundred-digit number

[kucharek]

http://www.timesonline.co.uk/article/0,,3-1373489,00.html
A MATHEMATICAL genius who struggled to pass his school exams has outwitted computers by setting a world record for mentally calculating the 13th root of a hundred-digit number.

Gert Mittring, a 38-year-old German who has doctorates in psychology and education, needed only 11.8 seconds to solve the puzzle.

Image at http://www.spiegel.de/img/0,1020,410887,00.jpg

Would like to know if he wrote down the number and then the clocking started or if the clocking started when he was shown the number.

Harald

[mickal555]

Wow that's amazing
If he had to write down the no. he would also set a record for fastest writing :o

BTW
http://www.spiegel.de/img/0,1020,410887,00.jpg
He looks scary :o

[Gullible Jones]

Anyone here know the method for calculating the nth root of a given number without the aid of any electronic devices? :P I've asked around, but I haven't found it...

[Glom]

He looks like Phil Cornwell.

[Moose]

Man, the only way I could ever come up with that answer in 11.8 seconds would be to read it straight off the answer card.

[frogesque]

Anyone here know the method for calculating the nth root of a given number without the aid of any electronic devices? :P I've asked around, but I haven't found it...

nth root algorithim (http://en.wikipedia.org/wiki/Shifting_nth-root_algorithm)

Don't ask me if it makes sense though :o - I only googled!

[Brady Yoon]

Wow. I don't see how that is humanly possible. Shows how great some of the geniuses are. :o

[Gullible Jones]

Thanks, Frogesque.

(Why didn't I check Wikipedia? D'oh!)

[Laguna]

Would like to know if he wrote down the number and then the clocking started or if the clocking started when he was shown the number.

Harald
The clocking started when he was shown the number.
He did not write it down.

[Nicolas]

Wow. I don't see how that is humanly possible. Shows how great some of the geniuses are.

I don't see it either, but I wouldn't call the man a genius from that fact alone. What he did is some mechanical-like ability. I don't know from this if he is just a humanoid calculator, or if he has great insight in mathematics (or other sciences) too.

Compare it to this: I consider someone who plays the piano perfectly not a genius, he is just very talented into playing it and most probably extremely trained.
A genius needs a "creation" term in it in my opinion, whether it is giving new insights or discoveries in science, or in writing new music.

This is subjective of course, but I believe a genius is a creator, not a recreator.

Apart from that, truly amazing from this man! (and being able to do this doesn't exclude the possibility being a genius at all!)

[Laguna]

By the way.
That man has an IQ of 145.

[Wally]

He looks like Phil Cornwell.

Not sure what Phil C. looks like, but I think the guy is the spittin' image of Quitan Taratino myself. Indeed, a scary looking individual in his own right! 8-[

[papageno]

I don't see it either, but I wouldn't call the man a genius from that fact alone. What he did is some mechanical-like ability. I don't know from this if he is just a humanoid calculator, or if he has great insight in mathematics (or other sciences) too.

Gauss was able to do this kind of calculations and he was a great mathematician.

[Makgraf]

Wow. I don't see how that is humanly possible. Shows how great some of the geniuses are. :o
National Review's resident mathematician/homophobe John Derbyshire explains it in a post here (http://www.nationalreview.com/thecorner/04_11_27_corner-archive.asp#046719):

Without wishing to detract at all from Herr Mittring's achievement, I note that this kind of thing isn't so astounding as it at first seems, and in fact is probably within the range of things anyone could do if he set out doggedly to do it.
Look: The average 100-digit number -- that would be around 5,000 trillion trillion trillion trillion trillion trillion trillion trillion, of course -- has a base-10 logarithm of 99.69897, so its 13th root has a log of 7.66915. That root is therefore around 47 million. So you only have to figure out 8 digits.
Memorized tables will get you 3 or 4 digits instantly. E.g. you can divide up all the 100-digit numbers to get the first 2 digits of their 13th roots:
Numbers beginning 10000000 thru 12654373 have 13th roots beginning with 41. Numbers beginning 12654377 thru 17182636 have 13th roots beginning with 42. Numbers beginning 17182641 thru 23167793 have 13th roots beginning with 43. ... etc., thru to Numbers beginning 93874803 thru 99999965 have 13th roots beginning with 49.
This is of the order of things that you can quite easily memorize. With a bit of serious effort you -- or me, or anyone -- could memorize the 3-digit equivalent, a list of 81 items. (I.e. for 13th roots beginning 412 to 492. The smallest number whose 13th power has 100 digits is 41,246,264; the biggest is 49,238,825.)
You can also very easily memorize the right-most digits of 13th powers. For numbers ending in 0, 1, 2, 3, 4, 5, 6, 7, 8, 9 they are, believe it or not: 0, 1, 2, 3, 4, 5, 6, 7, 8, 9. For example, the 13th power of 247 is 12,736,801,848,653,359,358,345,383,963,927. Again, you could extend this to two or more digits (though it gets tricky very quickly).
Once you have a good stock of memorized base points like this, a bit of fast trial & error will get you there.
(I've assumed here that the 13th root is a whole number. In this kind of competition, they invariably are.)

[electromagneticpulse]

By the way.
That man has an IQ of 145.

:o Last time i did an IQ test i came out with 132... I'm going to another world where i can atleast consider myself dumb and not brain dead :D

[jfribrg]

Anyone here know the method for calculating the nth root of a given number without the aid of any electronic devices? :P I've asked around, but I haven't found it...

Can one assume that the number given was a perfect 13th power?

Here is my way:

Given a number of exactly 100 digits, you know that the answer has 8 digits. Using my memorized table of common logarithms to 8 digits, and my ability to multiply numbers real fast in my head, calculate the answer: if n = x^(1/13), x = 10^(13*log x).

Memorizing a table of logs should be no problem to one of those folks who know the first zillion digits of pi.


If you know beforehand that you are dealing with exactly 100 digits and a 13th root, then you only have 9,541,334 perfect 13th powers. With some practice interpolating and multiplying 13th powers in your head, no problem.

[Normandy6644]

Wow. I don't see how that is humanly possible. Shows how great some of the geniuses are.

I don't see it either, but I wouldn't call the man a genius from that fact alone. What he did is some mechanical-like ability. I don't know from this if he is just a humanoid calculator, or if he has great insight in mathematics (or other sciences) too.

Compare it to this: I consider someone who plays the piano perfectly not a genius, he is just very talented into playing it and most probably extremely trained.
A genius needs a "creation" term in it in my opinion, whether it is giving new insights or discoveries in science, or in writing new music.

This is subjective of course, but I believe a genius is a creator, not a recreator.

Apart from that, truly amazing from this man! (and being able to do this doesn't exclude the possibility being a genius at all!)

I feel the same way. Not knowing much else about him makes it hard to decide what he actually could be considered. One hell of an accomplishment though I tell you that.