Enumerating Cryptarithms Using Deterministic Finite Automata
Formal Languages and Automata Theory
2018-08-01 v1 Data Structures and Algorithms
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 . Those DFAs can be used as complete catalogues of cryptarithms,whose applications include enumeration of and counting the exact numbers of cryptarithm instances with digits that admit base- solutions. Moreover, explicit formulas for and are given.
Keywords
Cite
@article{arxiv.1807.11580,
title = {Enumerating Cryptarithms Using Deterministic Finite Automata},
author = {Yuki Nozaki and Diptarama Hendrian and Ryo Yoshinaka and Takashi Horiyama and Ayumi Shinohara},
journal= {arXiv preprint arXiv:1807.11580},
year = {2018}
}