An Integer Linear Programming Model for the Evolomino Puzzle

TL;DR

This paper formalizes the Evolomino puzzle as an ILP model and demonstrates its effectiveness in generating and solving instances efficiently using a CP-SAT solver.

Contribution

It introduces a novel ILP formulation for Evolomino and an algorithm for generating unique, solvable puzzle instances.

Findings

CP-SAT solver solves 10x10 puzzles in under one second

Solver handles 18x18 puzzles within one minute

ILP model accurately encodes puzzle rules and constraints

Abstract

Evolomino is a pencil-and-paper logic puzzle published by the Japanese company Nikoli, renowned for culture-independent puzzles such as Sudoku, Kakuro, and Slitherlink. Its name reflects the core mechanic: the polyomino-like blocks drawn by the player must gradually "evolve" according to the directions indicated by arrows pre-printed on a rectangular grid. In this paper, we formalize the rules of Evolomino as an integer linear programming (ILP) model, encoding block evolution, connectivity, and consistency requirements through linear constraints. Furthermore, we introduce an algorithm for generating random Evolomino instances, utilizing this ILP framework to ensure solution uniqueness. Computational experiments on a custom benchmark dataset demonstrate that a state-of-the-art CP-SAT solver successfully handles puzzle instances of up to $10 \times 10$ within one second and up to $18 \times 18$ within one minute.