Mental Calculation Records: Extracting Roots
OFFICIAL RECORD LIST BY THE REKORD-KLUB SAXONIA
The records in this list are "standard calculation tasks". Record
breakers should try to break one of the records in our list instead of
creating new categories. It is very unlikely that new categories will
be added to our lists.
If you are going to break one of these records, please contact us.
Calculating the Square Root of a Six-Digit Number
The Rules
This
record is for the fastest time for an individual to calculate the
square roots of ten six-digit number to eight significant numbers
without a single error. The general
rules
for calculating records and the specific rules for the
square root category at the Mental Calculation World Cup apply.
The Records
7:37 min
|
Selçuk Soner Akgül
(Turkey) |
6 September 2009 |
Memoriad Turkey in Ankara |
6:37 min
|
Hakan Gürbaşlar (Turkey)
|
20 March 2010
|
Middle East Technical University
in Ankara
|
6:19 min
|
Selçuk Soner Akgül
(Turkey) |
2 June 2010
|
Nermin Mehmet
Çekiç Anadolu Lisesi, Ankara
|
4:55,05 min
|
Hakan Gürbaşlar (Turkey) |
17 December 2011
|
Ankara VIDEO |
| 2:43.05 min |
Priyanshi Somani (India) |
3 January 2012
|
Lourdes Covent School in Surat,
India
|
National records:
Spain: 11:06 min by Alberto Coto,
7 June 2010 at the Mental
Calculation World Cup in Magdeburg, Germany
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 general rules for calculating
records apply.
- 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.
Wim Klein
|
Gert Mittring
|
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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