Mental Calculation Records: Extracting Roots
OFFICIAL RECORD LIST BY THE REKORD-KLUB SAXONIA
The records in this list are "standard calculation tasks".
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Calculating the Square Root of a Six-Digit Number
The Rules
[Note: In future, no more records for single tasks will be
considered. The record category will be replaced with new records for
the fastest time to solve 10 tasks (without a break
between the tasks) correctly.]
This record is for the fastest time for an individual to calculate the
square root of a six-digit number to eight significant numbers.
- The record is a test of straightforward mental calculation. The calculator
should perform the calculation in his/her head without the aid of any other
person and without using a calculating machines, computers, etc. nor may
the calculator write the numbers down.
- The number whose square root is to be calculated should be randomly
selected by computer immediately prior to the calculation and should be
displayed to the calculator on a computer screen, board, screen or similar.
The number should be seen by the witnesses (see below) prior to being seen
by the competitor - it is important that the given number is not the square
of an integer nor should it be too close to the square of an integer.
- The calculator should write down the answer to the calculation to eight
significant figures (three before the decimal point and five after).
- The timing begins when the number becomes visible to the competitor
and ends at the end of writing the answer.
- In some cases, the calculator may dictate the answer - then the timing
ends as the calculator finishes dictating the answer.
- Two stop watches should be used: it would be appreciated these stopwatches
record in minutes and seconds and tenths of a second rather than hundredths
of an hour. At the end of the attempt the time should be taken as an average
of the two watches.
- The name of the person making the attempt should be given, along with
the date and place.
The witnesses should
be persons with a background in mental arithmetic capable of judging whether
the number randomly selected is either the square of an integer or is too
close to the square of an integer.
The Records
63.8 sec M. Hari Prasad (India) 30-10-1999 Bangalore
51.8 sec Gert Mittring (Germany) 2000 Linz
44.7 sec Gert Mittring (Germany) 7- 7-2000 Flensburg
Wim Klein
|
Gert Mittring
|
13th root of a 100 digit number
The Rules
[Note: In future, no more records for single tasks will be
considered. The record category will be replaced with new records for
the fastest time to solve 9 tasks or 3 tasks (see below)]
- The record
is a standard test of straightforward mental calculation for
high order integer roots. The calculator should perform the calculation
in his/her head without the aid of any other person and without using a
calculating machines, computers, etc. nor may the calculator write down
any intermediate results which are not part of the final result.
- The numbers of 100 digits whose 13th root is to be calculated
should be randomly selected by computer immediately prior to the
calculation. It is important that the given numbers are
the 13th power of integer numbers between 41246264 and 49238826, both inclusive. They should be displayed to the
calculator on a computer screen, board, sheet of paper, screen or similar.
- 9 tasks-category: One of those numbers must end in 1, one must end in 2,
... , and one must end in 9. (The
candidate cannot rely on an ordering of the tasks: The power ending in one does not have to be the
first one in the list etc.)
- 3 tasks-category: One of those numbers must end in 5, the second one must end in 1,3,7 or 9, and the third one must end in 2,4,6 or 8. (The
candidate cannot rely on an ordering of the tasks: The power ending in 5 does not have to be the
first one in the list etc.)
- The calculator has to write down the answers.
- The timing begins when the number becomes visible to the competitor and
ends at the end of writing the answer.
- In some cases, the calculator may dictate the answers - then the timing
ends as the calculator finishes dictating the last result.
- Two stop watches should be used: it would be appreciated these stopwatches
record in minutes and seconds and tenths of a second rather than hundredths of
an hour. At the end of the attempt the time should be taken as an average of
the two watches.The name of the person making the attempt should be given, along with the
date and place.
Willem Klein (Netherlands) improved his record for a single task five
times - from 322 seconds in 1975 to finally 88.8 seconds in 1981. Later
both Gert Mittring (Germany) and Alexis Lemaire
(France) solved a single task in less than 15 seconds. Because the
difficulty of the problem depends on the 100-digit number, no more
records for solving a single task will be considered.
23rd root of a 200 digit number
(The 200 digit number should be a number raised to the 23rd power.)
50 sec Shakuntala Devi (India) 1977 Dallas
In
2002, Gert Mittring calculated the 23rd root of a 200 digit number in
40.83 seconds. While the attempt was not officially verified, there is
no doubt that he has done the calculation in this time.
No more
records for this category will be considered.
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