Move-minimizing puzzles and diamond-colored modular/distributive lattices

TL;DR

This paper explores move-minimizing puzzles modeled as diamond-colored modular or distributive lattices, providing explicit solutions through a novel interpretation of order-theoretic combinatorics.

Contribution

It introduces a new approach to solving move-minimizing puzzles by encoding them as specific lattices and applying order-theoretic methods.

Findings

Explicit solutions for certain move-minimizing puzzles

New interpretation of order-theoretic combinatorics

Connection between puzzles and lattice theory

Abstract

The move-minimizing puzzles presented here are certain types of one-player combinatorial games that are shown to have explicit solutions whenever they can be encoded in a certain way as diamond-colored modular or distributive lattices. Our work here is founded in a new interpretation of some routine and elementary order-theoretic combinatorics.