# Solving Zebra Puzzles Using Constraint-Guided Multi-Agent Systems

arXiv: https://arxiv.org/abs/2407.03956 · HTML: https://mlsanity.com/paper/2407.03956/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Placed in Reasoning benchmarks and evaluation, one of 17 directions in LLM reasoning.
- Builds on 8 of its 23 references that are in the map.
- First posted on arXiv 4 Jul 2024.

## Placed in

- LLM reasoning / [Reasoning benchmarks and evaluation](https://mlsanity.com/lr/reasoning-benchmarks-and-evaluation/)
- LLM agents and tool use / [Educational agents and math problem solving](https://mlsanity.com/agents/educational-agents-and-math-problem-solving/)

## Builds on (most cited first, 8 of 8)

- [A Survey on Large Language Model based Autonomous Agents](https://mlsanity.com/paper/2308.11432/) (2023)
- [Program of Thoughts Prompting: Disentangling Computation from Reasoning for Numerical Reasoning Tasks](https://mlsanity.com/paper/2211.12588/) (2022)
- [Language Agent Tree Search Unifies Reasoning Acting and Planning in Language Models](https://mlsanity.com/paper/2310.04406/) (2023)
- [Agent AI: Surveying the Horizons of Multimodal Interaction](https://mlsanity.com/paper/2401.03568/) (2024)
- [Learning from Dialogue after Deployment: Feed Yourself, Chatbot!](https://mlsanity.com/paper/1901.05415/) (2019)
- [SatLM: Satisfiability-Aided Language Models Using Declarative Prompting](https://mlsanity.com/paper/2305.09656/) (2023)
- [Integrating Graphs with Large Language Models: Methods and Prospects](https://mlsanity.com/paper/2310.05499/) (2023)
- [Measuring reasoning capabilities of ChatGPT](https://mlsanity.com/paper/2310.05993/) (2023)

## Built on by (most cited first, 4 of 4)

- [Logic.py: Bridging the Gap between LLMs and Constraint Solvers](https://mlsanity.com/paper/2502.15776/) (2025)
- [A Reality Check of Language Models as Formalizers on Constraint Satisfaction Problems](https://mlsanity.com/paper/2505.13252/) (2025)
- [Evaluating Implicit Biases in LLM Reasoning through Logic Grid Puzzles](https://mlsanity.com/paper/2511.06160/) (2025)
- [VeryTrace: Verifying Reasoning Traces through Compilable Formalism and Structured Verification](https://mlsanity.com/paper/2606.24124/) (2026)

## Abstract (arXiv)

Prior research has enhanced the ability of Large Language Models (LLMs) to solve logic puzzles using techniques such as chain-of-thought prompting or introducing a symbolic representation. These frameworks are still usually insufficient to solve complicated logical problems, such as Zebra puzzles, due to the inherent complexity of translating natural language clues into logical statements. We introduce a multi-agent system, ZPS, that integrates LLMs with an off the shelf theorem prover. This system tackles the complex puzzle-solving task by breaking down the problem into smaller, manageable parts, generating SMT (Satisfiability Modulo Theories) code to solve them with a theorem prover, and using feedback between the agents to repeatedly improve their answers. We also introduce an automated grid puzzle grader to assess the correctness of our puzzle solutions and show that the automated grader is reliable by evaluating it in a user-study. Our approach shows improvement in all three LLMs we tested, with GPT-4 showing 166% improvement in the number of fully correct solutions.