Enumeration of cryptarithms using deterministic finite automata

Research output: Chapter in Book/Report/Conference proceedingConference contribution


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 Gk(n) of cryptarithm instances with n digits that admit base-k solutions. Moreover, explicit formulas for G2(n) and G3(n) are given.

Original languageEnglish
Title of host publicationImplementation and Application of Automata - 23rd International Conference, CIAA 2018, Proceedings
EditorsCezar Campeanu
PublisherSpringer Verlag
Number of pages13
ISBN (Print)9783319948119
Publication statusPublished - 2018
Event23rd International Conference on Implementation and Application of Automata, CIAA 2018 - Charlottetown, Canada
Duration: 2018 Jul 302018 Aug 2

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume10977 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349


Other23rd International Conference on Implementation and Application of Automata, CIAA 2018


  • Alphametics
  • Automaton
  • Cryptartihms
  • DFA
  • Enumeration

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Computer Science(all)


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