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Post subject: NEWS: Maths whiz sets record for mental calculation
 Posted: Nov 25, 2004 - 01:15 PM
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Site Admin
Joined: Jul 11, 2003
Posts: 106
Location: Charlottesville, Virginia, USA
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This is almost unbelievable...
13th root in 12secs best ever
Roger Boyes, Berlin
November 26, 2004
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.
The number was chosen at random by Albrecht Beutelspacher, director of the Mathematics Museum at Giessen, near Frankfurt. Two umpires ensured fair play. Spectators using electronic calculators were left minutes behind.
The 13th root is the number which, when multiplied by itself 12 times, equals the number selected. The sum to find it is beyond the range of most everyday calculators.
The Guinness Book of Records may not accept the record, since it no longer recognises root calculations of random numbers.
Even so, the German mathematical puzzler holds 24 recognised world records.
His performance at Giessen pushes back the boundaries of mental calculation.
The record for calculating the 13th root of a hundred-digit figure was first set in 1975 by Dutchman Willem Klein, who took 320 seconds. Klein refined his technique and by 1981 had managed to get the calculation down to 89 seconds.
Dr Mittring took up the challenge after Klein's death. He sliced 50 seconds off Klein's achievement and yesterday came close to a single-digit time.
Dr Mittring, whose maths teacher once described him as "disturbingly unsatisfactory", has become an astonishing example of the capacity of the human brain.
His achievements include memorising a 22-decimal figure inside four seconds and 30 binary figures within three seconds. He has also identified, within 38 seconds, the days of the week of 20 random dates in a century.
Dr Mittring emphasises that there are no tricks involved. "I don't train before an event," he said. "When I'm given a number, I just think of an elegant problem-solving algorithm and the result comes straight away."
The Times
Link to story
http://www.theaustralian.news.com.au/common/story_page/0,5744,11501917%255E601,00.html |
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Post subject:
Posted: Nov 27, 2004 - 05:39 PM
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Joined: Nov 09, 2003
Posts: 733
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Clay, I am impressed by the performance of Dr. Gert Mittring, as reported by the article reported by Roger Boyes from Berlin, and kindly linked by you.
He is definitely a genius, and he has certainly attained a very high level in his mental calculations, developed a method (not a trick), and has very well practised his method. This is evidenced by the fact that he does not need to practise beforehand, which implies that the results do not come by chance!
Just like if we were to be requested to count the number of grains of sand at a beach,
most of us would stare on the white sand and say, how would I know. This is perfectly normal. For those of us who believe that it is possible, we will TRY and develop a method. Perhaps not the exact number, perhaps not even nearly exact, but it will be an approximation. From the approximation, we refine our method, and get even closer. This is how geniuses like Dr. Mittring work.
====================================================================
If we try to take up his challenge, this is how I would start.
First, looking at the 13th root, by very simple calculations, we understand that:
ANY NUMBER RAISED TO THE 13TH POWER WILL HAVE THE LAST DIGIT OF THE RESULT EQUAL TO THAT OF THE ORIGINAL NUMBER.
That settles the last digit of the answer, simply by copying the last digit of the number to be extracted 13th root as the last digit of our answer!
Next, we would like to find out within what range the answers should be, given that the original number has to be a 100 digit number. Therefore the logarithm (to base 10) of the original number must be between 99.000 and 99.9999999...
Using an ordinary calculator, we calculate the numbers
99/13=7.61538462.. and 7.69230769230...
Raising 10 to these powers gives us the lower and upper limits as:
41246264 and 49238826.
In fact, the answers are as follows:
41246264 ** 13=1000000053891531265062238747077907560690804374410559722392499871913587301621661365915461814157574144
49238826 ** 13 =9999999162880950507644688918524814522347242627239243189376115437857450758590978444820365074927230976
So we know that the answers are 8 digit figures, starting with 4, in fact, between 41246264 and 49238826, with the last digit equal to the last digit of the given number!
We are not that far off!
With this information in mind, now we are going to find the 13th root of a given 100-digit number!
2345813452573965450990121027421105301917006585675372430552395152492628208920201161613694616524029952
If you are a mathematician, you probably have access to superior software such as Mathematica that will let you get the 13th root in a flash. If you are like the rest of us, with at best a good calculator in hand, this is how we could proceed:
We will find the logarithm (to base 10) of the number using the calculator. We will not be able to enter the number into most calculators, but we will do it approximately by noting that the number is nothing more than
2.3458134525739..*10^99 (that makes a number of 100 digits)
The logarithm is simply 99+log10(2.3458134525739)=99.3702934725
Divide the number by 13 to get 7.643868729
Calculate 10^(7.643868729) to get 44042172, which is the correct answer, noting that the last digit corresponds with the last digit of the original number!
So here it is, if you were with Dr. Mittring at the performance, with a calculator in hand, you could have beaten him with your answer in less than 11.8 seconds!
44042172 ** 13 =2345813452573965450990121027421105301917006585675372430552395152492628208920201161613694616524029952
Happy Mental Calculations!
Note:
The above calculations for raising to the power of 13 are thanks to a multi-digit calculator available at the following site:
http://www.mathpath.net
look under Arbitrary Precision Calculator.
The calculator can do calculations of thousands of digits. The number of digits of precision is YOUR choice.
If you want more practice (to compete with Dr. Mittring!), you could raise numbers between 41246264 and 49238826 to the 13th power and try your hand with the above method. |
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Post subject:
Posted: Nov 28, 2004 - 06:51 AM
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Site Admin
Joined: Jul 11, 2003
Posts: 106
Location: Charlottesville, Virginia, USA
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mathmate, you make it seem too easy!
Seriously, you should publish that on the homepage. That's a great article. I can publish it if you want (and of course credit you as author). Let me know. It's too good to get buried in the forum. |
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Post subject:
Posted: Nov 28, 2004 - 06:33 PM
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Joined: Nov 09, 2003
Posts: 733
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Clay, your kind words are much appreciated.
As suggested, and in the next few days, I will submit an article on the homepage, most probably after a little rewrite including some context. At that time, you can decide if you want to retain this reply in the forum or not.
Alternatively, you could move it to the home page for now, and replace with my new article when it will be submitted, which will probably not before four or five days. |
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Post subject:
Posted: Nov 29, 2004 - 07:20 AM
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Site Admin
Joined: Jul 11, 2003
Posts: 106
Location: Charlottesville, Virginia, USA
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mathmate, I'll wait for the submitted article. No hurry. 
BTW, I didn't mean to impose on you! I hope I haven't caused you too much work. You're certainly welcome to decline altogether. It's just that I could tell you put a great deal of effort into your reply and thought maybe it should be preserved as an article. Take care, Clay |
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