Pandigital number

A pandigitale number ( from Greek παν: " each" and digital) is a decimal integer that contains each of the ten digits 0 through 9 exactly once. The first digit must not be 0.

Pandigitale numbers have a real meaning neither in mathematics nor in any field of application. They are mostly used as a curiosity in mathematical puzzles on the type of Latin squares, or Sudokus.

An example is the number 1,748,592,603th

Each pandigitale number has the sum of the digits 45 and is therefore divisible by 9:

There are a total of 9 x 9! = 3265920 pandigitale numbers: There are 9 possibilities for the first digit (since the zero is excluded ), 9 for the second ( since the first digit is excluded), ( can not be used the first two digits must again ) 8 for the third 7 for fourth, etc.

The first pandigitalen numbers are 1023456789, 1023456798, 1023456879, 1023456897, 1023456978 ( sequence A050278 in OEIS ).

MultiDigital

A more general definition of pandigitalen numbers is the following: A number or mathematical expression that contains each digit exactly once to a base. In France, such numbers are also called multi- digital, the numbers to the base 10 decadigital.

For base 4 1320 pandigitale a number and 2 1 = 3 0 pandigitale a sum.

Pandigitale breaks

Pandigitale fractures are fractures that contain the digits 1 through 9 exactly once.

Examples:

Special pandigitale numbers

3816547290 is the only pandigitale number, wherein the first n digits (read as numbers) are respectively divisible by n; the first digit by 1, the first two digits by 2, the first three digits by 3, etc.:

9,814,072,356 is the largest pandigitale square number. Its root is the " rotating " number 66099th