Tool to generate Cartesian products of lists/sets by combining the elements to generate the complete list of possible choices.

Cartesian Product - dCode

Tag(s) : Combinatorics

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

A suggestion ? a feedback ? a bug ? an idea ? *Write to dCode*!

A Cartesian product is a combination of elements from several sets. The product is written with the symbol `×`. It is the totality of the possible combinations among the sets of elements.

Enter the sets (1 per line) in the generator table and click on generate.

__Example:__ Generation of all playing card figures (jack, queen, king) of each color (spade, heart, diamond, club)

The first set consists of the 3 figures {`J`,`Q`,`K`}, the second set of the 4 colors {`♠`,`♥`,`♦`,`♣`}.

The Cartesian product is:

J | ♠ |

J | ♥ |

J | ♦ |

J | ♣ |

Q | ♠ |

Q | ♥ |

Q | ♦ |

Q | ♣ |

K | ♠ |

K | ♥ |

K | ♦ |

K | ♣ |

The cardinality (total number of combinations) is equal to the multiplication of the cardinality of each set.

__Example:__ A garment with 3 color choices and 5 sizes will have $ 3 \times 5 = 15 $ different possibilities

__Example:__ A padlock with 4 wheels that can define a 4-letter code (26 possible letters for each wheel) will have a cardinality of $ 26 \times 26 \times 26 \times 26 = 456976 $ possible words.

dCode retains ownership of the "Cartesian Product" source code. Except explicit open source licence (indicated Creative Commons / free), the "Cartesian Product" algorithm, the applet or snippet (converter, solver, encryption / decryption, encoding / decoding, ciphering / deciphering, breaker, translator), or the "Cartesian Product" functions (calculate, convert, solve, decrypt / encrypt, decipher / cipher, decode / encode, translate) written in any informatic language (Python, Java, PHP, C#, Javascript, Matlab, etc.) and all data download, script, or API access for "Cartesian Product" are not public, same for offline use on PC, mobile, tablet, iPhone or Android app!

Reminder : dCode is free to use.

The copy-paste of the page "Cartesian Product" or any of its results, is allowed (even for commercial purposes) as long as you cite dCode!

Exporting results as a .csv or .txt file is free by clicking on the *export* icon

Cite as source (bibliography):

*Cartesian Product* on dCode.fr [online website], retrieved on 2023-05-31,

cartesian,product,combination,list

https://www.dcode.fr/cartesian-product

© 2023 dCode — The ultimate 'toolkit' to solve every games / riddles / geocaching / CTF.

Feedback