13th root
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Extracting the 13th root of a number is a famous category for the mental calculation world records. The challenge consists of being given a large number (possibly over 100 digits) and asked to return the number that equals it when multiplied by itself 13 times. For example, the 13th root of 8,192 is 2 and the 13th root of 96,889,010,407 is 7.
Properties of the challenge
Extracting the 13th root has certain properties. One is that the 13th root of a number is much smaller: a 13th root will have approximately 1/13th the number of digits. Thus the 13th root of a 100-digit number only has 8 digits and the 13th root of a 200-digit number will have 16 digits. Further, the last digit of the 13th root is always the same as the last digit of the power.
For the 13th root of a 100-digit number there are 7992563 possibilities, in the range 41246264 – 49238826. This is considered a relatively easy calculation. There are 393544396177593 possibilities, in the range 2030917620904736 – 2424462017082328, for the 13th root of a 200-digit number. This is considered a difficult calculation.
Records
The Guinness Book of World Records has published records for extracting the 13th root of a 100-digit number. All world records for mentally extracting a 13th root have been for numbers with an integer root.
- The first record was 23 minutes by De Grote(Mexico).
- The most published time was at one time 88.8 seconds by Klein(Netherlands).
- Gert Mittring calculated it in 38 seconds.
- Alexis Lemaire has broken his record with the 13.55 seconds. This is the last official world record for extracting the 13th root of a 100-digit number.
- Gert Mittring broke this record unofficially with 11.8 seconds, documented by Prof. Dr. Beuteolspacher, Mathematikum Giessen.
- Alexis Lemaire broke this record unofficially 6 times, twice within 4 seconds the best was 3.625 seconds, at the presidency of the University of Reims
- Alexis Lemaire has also set the first world record for the 13th root of a 200-digit number: 513.55 seconds and 742 attempts on April 6th, 2005, and broken it with 267.77 seconds and 577 attempts on June 3rd, 2005:
- the same day, Alexis Lemaire has also set in front of official witnesses an unofficial record of 113 seconds and 40 attempts
External links
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