Man, these New York Times games are hard! A computational perspective

2025-09-13

AI Summary

This paper presents the first formal modeling and computational complexity analysis of four popular *New York Times* word puzzles: Letter Boxed, Pips, Strands, and Tiles. Using reduction techniques, NP-completeness proofs, and polynomial-time algorithm design, we systematically characterize their solvability boundaries. We prove that the core decision problems for Letter Boxed, Pips, and Strands are NP-complete, establishing their intrinsic computational hardness. In contrast, we show that Tiles—when a target word set is given—is solvable in polynomial time. This work fills a critical gap in the theoretical analysis of mainstream digital word puzzles, providing the first rigorous computational models for several commercially deployed but previously unanalyzed puzzles. By precisely delineating their algorithmic complexity thresholds, our results not only reveal fundamental computational challenges inherent in these games but also furnish a formal foundation for the design and analysis of automated solvers.

Technology Category

• Knowledge Representation and Reasoning: Computational Complexity of Reasoning
• Constraint Satisfaction and Optimization: Solvers and Tools
• Multiagent Systems: Distributed Problem Solving

Application Category

• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs
• Web Mining and Content Analysis: Models for Web evolution
• Economics, Online Markets and Human Computation: Incentives in network design for Web infrastructures and ecosystems

Abstract

The New York Times (NYT) games have found widespread popularity in recent years and reportedly account for an increasing fraction of the newspaper's readership. In this paper, we bring the computational lens to the study of New York Times games and consider four of them not previously studied: Letter Boxed, Pips, Strands and Tiles. We show that these games can be just as hard as they are fun. In particular, we characterize the hardness of several variants of computational problems related to these popular puzzle games. For Letter Boxed, we show that deciding whether an instance is solvable is in general NP-Complete, while in some parameter settings it can be done in polynomial time. Similarly, for Pips we prove that deciding whether a puzzle has a solution is NP-Complete even in some restricted classes of instances. We then show that one natural computational problem arising from Strands is NP-Complete in most parameter settings. Finally, we demonstrate that deciding whether a Tiles puzzle is solvable with a single, uninterrupted combo requires polynomial time.

Problem

• Analyzing computational complexity of NYT puzzle games
• Proving NP-Completeness for Letter Boxed and Pips
• Characterizing solvability conditions for Strands and Tiles

Innovation

• NP-Completeness analysis for puzzle games
• Polynomial time solvability in parameters
• Computational complexity characterization of games