Cryptarithms: A Non-Programming Approach Using Excel

Abstract

This paper presents a method for solving cryptarithms (variously known as alphametics, crypto-arithmetics, arithmetical restorations, and verbal arithmetic) using Microsoft Excel along with the Solver add-in. In order to make it suitable for classroom presentation, elements of the method are introduced incrementally, first as a linear program, then as an integer linear program, and finally as a integer linear program with “all different” variables. Unlike other approaches discussed in the literature (the “brute force” method, logic programming, and parallel genetic algorithms), this method does not require a knowledge of computer programming. It also introduces users of Excel to the often neglected integer and alldifferent constraints, as well as the increase in computational time associated with these constraints.