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 min
|
Hakan Gürbaşlar (Turkey) |
17 December 2011
|
Ankara VIDEO |
| 2:43 min |
Priyanshi Somani (India) |
3 January 2012
|
Lourdes Covent School in
Surat, India
|
| 2:06.8 min |
Rhea Sandeep Shah (India) |
31 August 2013
|
Turkish Memoriad, Ankara
|
| 1:33.8 min |
Rhea Sandeep Shah (India) |
31 August 2013 |
Turkish Memoriad, Ankara |
| 1:30.0 min |
Rhea Sandeep Shah (India) |
31 August 2013 |
Turkish Memoriad, Ankara |
| 1:07.5 min |
Granth Rakesh Thakkar (India) |
2 September 2013
|
Memoriad Center, Ankara
|
1:04.9 min
|
Granth Rakesh Thakkar (India)
|
7 October 2014
|
Dresden
|
1:01.9 min
|
Granth Rakesh Thakkar (India)
|
7 October 2014
|
Dresden
|
Additional statistics and national records can be found in the mental calculation world
ranking list.
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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