### Abstract

A cryptarithm is a mathematical puzzle where given an arithmetic equation written with letters rather than numerals, a player must discover an assignment of numerals on letters that makes the equation hold true. In this paper, we propose a method to construct a DFA that accepts cryptarithms that admit (unique) solutions for each base. We implemented the method and constructed a DFA for bases k≤ 7. Those DFAs can be used as complete catalogues of cryptarithms, whose applications include enumeration of and counting the exact numbers G_{k}(n) of cryptarithm instances with n digits that admit base-k solutions. Moreover, explicit formulas for G_{2}(n) and G_{3}(n) are given.

Original language | English |
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Title of host publication | Implementation and Application of Automata - 23rd International Conference, CIAA 2018, Proceedings |

Editors | Cezar Campeanu |

Publisher | Springer Verlag |

Pages | 286-298 |

Number of pages | 13 |

ISBN (Print) | 9783319948119 |

DOIs | |

Publication status | Published - 2018 Jan 1 |

Event | 23rd International Conference on Implementation and Application of Automata, CIAA 2018 - Charlottetown, Canada Duration: 2018 Jul 30 → 2018 Aug 2 |

### Publication series

Name | Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) |
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Volume | 10977 LNCS |

ISSN (Print) | 0302-9743 |

ISSN (Electronic) | 1611-3349 |

### Other

Other | 23rd International Conference on Implementation and Application of Automata, CIAA 2018 |
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Country | Canada |

City | Charlottetown |

Period | 18/7/30 → 18/8/2 |

### Keywords

- Alphametics
- Automaton
- Cryptartihms
- DFA
- Enumeration

### ASJC Scopus subject areas

- Theoretical Computer Science
- Computer Science(all)

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## Cite this

*Implementation and Application of Automata - 23rd International Conference, CIAA 2018, Proceedings*(pp. 286-298). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 10977 LNCS). Springer Verlag. https://doi.org/10.1007/978-3-319-94812-6_24