Pandigital number
A pandigital number (from the Greek παν: “each” and digital in the sense of being represented by digits) is a decimal whole number that contains each of the ten digits from 0 to 9 exactly once. The first digit must not be 0.
Pandigital numbers have no real meaning in mathematics or in any other field of application. They are mostly used as a curiosity in mathematical puzzles like Latin squares or Sudokus .
An example is the number 1748592603.
Every pandigital number has the checksum 45 and is therefore divisible by 9 :
- 0 + 1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 = 45
There are 9 9 in total! = 3265920 pandigital numbers: There are 9 possibilities for the first digit (because the zero is excluded), 9 for the second (because the first digit is excluded), 8 for the third (the first two digits must not be used again) , 7 for the fourth, etc.
The first pandigital numbers are 1023456789, 1023456798, 1023456879, 1023456897, 1023456978 (sequence A050278 in OEIS ).
Multi-digital
A more general definition of pandigital numbers is as follows: A number or a mathematical expression that contains each digit on a base exactly once. In France, those numbers are also multi digitally called the numbers to base 10 decadigital .
For base 4, 1320 is a pandigital number and 2 + 1 = 3 + 0 is a pandigital sum.
Pandigital breaks
Pandigital fractions are fractions that contain the digits 1 to 9 exactly once.
Examples:
- or or
Pandigital formulas
Pandigital formulas are formulas that contain the digits 1 to 9 exactly once.
Examples:
approximates Euler's number e exactly to 18457734525360901453873570 decimal places.
Special pandigital numbers
3,816,547,290 is the only pandigital number in which the first n digits (read as numbers) are each divisible by n ; the first digit through 1, the first two digits through 2, the first three digits through 3, etc .:
3 | → divisible by 1 |
38 | → divisible by 2 |
381 | → divisible by 3 |
3816 | → divisible by 4 |
38165 | → divisible by 5 |
381654 | → divisible by 6 |
3816547 | → divisible by 7 |
38165472 | → divisible by 8 |
381654729 | → divisible by 9 |
3816547290 | → divisible by 10 |
9,814,072,356 is the largest pandigital square number. Its square root is the “rotatable” number 99066.
See also
Web links
- Eric W. Weisstein : Pandigital Number . In: MathWorld (English).
- Eric W. Weisstein : Pandigital Fraction . In: MathWorld (English).
Individual evidence
- ↑ immeron.edu
- ↑ johndcook.com
- ^ The Nine Digits Page with some Ten Digits (pandigital) exceptions . World! Of Numbers; accessed on March 2, 2014.
- ↑ Gleick: The information . 1st edition. Redlineverlag, 2011, ISBN 978-3-86881-312-8 , p. 366