Tool using the Kaprekar algorithm. It uses an integer N, and arranges its digits in ascending and descending order, before subtracting them.

Kaprekar Algorithm - dCode

Tag(s) : Mathematics, Algorithm

dCode is free and its tools are a valuable help in games, puzzles and problems to solve every day!

You have a problem, an idea for a project, a specific need and dCode can not (yet) help you? You need custom development? *Contact-me*!

Sponsored ads

Tool using the Kaprekar algorithm. It uses an integer N, and arranges its digits in ascending and descending order, before subtracting them.

The Kaprekar routine from a number \( N \) consists of creating 2 other numbers \( N_1 \) and \( N_2 \) by arranging the digits of \( N \) by sorting them in ascending order to \( N_1 \) and decreasing for \( N_2 \). Kaprekar then forms a new number \( N \) such that \( N_2-N_1 = N \) and repeats the process until arriving at a previously found number.

Example: \( N = 7533 \), \( N_1 = 3357 \), \( N_2 = 7533 \), replace \( N \) with \( 7533 - 3357 = 4176 \)

\( N = 4176 \), \( N_1 = 1467 \), \( N_2 = 7641 \) then replace \( N \) with \( 7641 - 1467 = 6174 \)

\( N = 6174 \), \( N_1 = 1467 \), \( N_2 = 7641 \) replace \( N \) with \( 7641 - 1467 = 6174 \), which creates an infinite loop on the constant 6174, which is the Kaprekar constant for 4 digits.

Loops are repetition of values or constants that appears in the algorithm depending on the size of the number \( N \).

Number of digits | Constant/Loop |
---|---|

3 | 495 |

4 | 6174 |

5 | 53955, 59994 or 62964, 71973, 83952, 74943 or 61974, 82962, 75933, 63954 |

6 | 420876, 851742, 750843, 840852, 860832, 862632, 642654 or 631764 or 549945 |

7 | 7509843, 9529641, 8719722, 8649432, 7519743, 8429652, 7619733, 8439552 |

8 | 43208766, 85317642, 75308643, 84308652, 86308632, 86326632, 64326654 or 64308654, 83208762, 86526432 or 97508421 or 63317664 |

When one of these numbers is reached, either it remains constant or it follows the cycle by looping to infinity.

dCode retains ownership of the source code of the script Kaprekar Algorithm online. Except explicit open source licence (indicated Creative Commons / free), any algorithm, applet, snippet, software (converter, solver, encryption / decryption, encoding / decoding, ciphering / deciphering, translator), or any function (convert, solve, decrypt, encrypt, decipher, cipher, decode, code, translate) written in any informatic langauge (PHP, Java, C#, Python, Javascript, Matlab, etc.) which dCode owns rights will not be given for free. To download the online Kaprekar Algorithm script for offline use on PC, iPhone or Android, ask for price quote on contact page !

kaprekar,constant,algorithm,routine,495,6174,digit,number,sort,order,sequence

Source : https://www.dcode.fr/kaprekar-algorithm

© 2018 dCode — The ultimate 'toolkit' to solve every games / riddles / geocaches. dCode

Feedback