mahdi-torabian/cryptarithmetic

Solve cryptarithmetic addition puzzles using the LeapHybridCQMSampler.

Cryptarithmetic Addition

Cryptarithmetic puzzles are logical puzzles where the goal is to have unique assignments of digits to letters, such that the mathematical expression holds true. This demo only runs with addition puzzles.

Usage

To run this demo, execute:

python cryptarithm.py --filename path/to/your/file.txt

For simplicity and to establish convention, ensure all letters are capitalized, that the puzzle be written on the first line of the file, and that no more than 10 unique letters are used in total.

For example:

python cryptarithm.py --filename puzzle_files/example1.txt

Could produce:

Solution found for SEND + MORE = MONEY, 9567 + 1085 = 10652

There are three puzzle files provided in the puzzle_files directory. If no puzzle file is specified, puzzle_files/example1.txt is used by default.

Code Overview

Constraints considered in problem formuation:

1. The first constraint is that the left-hand side must be equal to the right-hand side.
2. Assignments of digits to letters must be unique, thus a puzzle may contain no more than 10 unique letters. This is expressed as a series of encoded not-equal constraints.
3. The first letters must be assigned a non-zero digit, unless the puzzle contains one letter words.

References

Wiki page on verbal arithmetic.

License

Released under the Apache License 2.0. See license here.