Enumerating cryptarithms using deterministic finite automata

Yuki Nozaki, Diptarama Hendrian, Ryo Yoshinaka, Takashi Horiyama, Ayumi Shinohara

Research output: Contribution to journalArticlepeer-review


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
JournalUnknown Journal
Publication statusPublished - 2018 Jul 26

ASJC Scopus subject areas

  • General

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