# LogicPuzzleRL: Cultivating Robust Mathematical Reasoning in LLMs via Reinforcement Learning

arXiv: https://arxiv.org/abs/2506.04821 · HTML: https://mlsanity.com/paper/2506.04821/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- Placed in Reinforcement learning for reasoning, one of 17 directions in LLM reasoning.
- Builds on 15 of its 19 references that are in the map.
- First posted on arXiv 5 Jun 2025.

## Placed in

- LLM reasoning / [Reinforcement learning for reasoning](https://mlsanity.com/lr/reinforcement-learning-for-reasoning/)

## Builds on (most cited first, 15 of 15)

- [Training Verifiers to Solve Math Word Problems](https://mlsanity.com/paper/2110.14168/) (2021)
- [DeepSeek-R1: Incentivizing Reasoning Capability in LLMs via Reinforcement Learning](https://mlsanity.com/paper/2501.12948/) (2025)
- [Measuring Mathematical Problem Solving With the MATH Dataset](https://mlsanity.com/paper/2103.03874/) (2021)
- [Kimi k1.5: Scaling Reinforcement Learning with LLMs](https://mlsanity.com/paper/2501.12599/) (2025)
- [OlympiadBench: A Challenging Benchmark for Promoting AGI with Olympiad-Level Bilingual Multimodal Scientific Problems](https://mlsanity.com/paper/2402.14008/) (2024)
- [Mastering Chess and Shogi by Self-Play with a General Reinforcement Learning Algorithm](https://mlsanity.com/paper/1712.01815/) (2017)
- [Instruction Tuning with GPT-4](https://mlsanity.com/paper/2304.03277/) (2023)
- [Towards Large Reasoning Models: A Survey of Reinforced Reasoning with Large Language Models](https://mlsanity.com/paper/2501.09686/) (2025)
- [DeepSeek-Prover-V2: Advancing Formal Mathematical Reasoning via Reinforcement Learning for Subgoal Decomposition](https://mlsanity.com/paper/2504.21801/) (2025)
- [ZebraLogic: On the Scaling Limits of LLMs for Logical Reasoning](https://mlsanity.com/paper/2502.01100/) (2025)
- [Kimina-Prover Preview: Towards Large Formal Reasoning Models with Reinforcement Learning](https://mlsanity.com/paper/2504.11354/) (2025)
- [AIMO-2 Winning Solution: Building State-of-the-Art Mathematical Reasoning Models with OpenMathReasoning dataset](https://mlsanity.com/paper/2504.16891/) (2025)
- [Gold-medalist Performance in Solving Olympiad Geometry with AlphaGeometry2](https://mlsanity.com/paper/2502.03544/) (2025)
- [Puzzle Solving using Reasoning of Large Language Models: A Survey](https://mlsanity.com/paper/2402.11291/) (2024)
- [Leanabell-Prover: Posttraining Scaling in Formal Reasoning](https://mlsanity.com/paper/2504.06122/) (2025)

## Built on by (most cited first, 5 of 5)

- [Do LLMs Overthink Basic Math Reasoning? Benchmarking the Accuracy-Efficiency Tradeoff in Language Models](https://mlsanity.com/paper/2507.04023/) (2025)
- [PR-CAD: Progressive Refinement for Unified Controllable and Faithful Text-to-CAD Generation with Large Language Models](https://mlsanity.com/paper/2604.19773/) (2026)
- [When RL Suppresses Its Own Vocabulary: Recovering Reasoning Diversity in Puzzle-to-Math Transfer](https://mlsanity.com/paper/2605.29190/) (2026)
- [Step-by-Step Optimization-like Reasoning in LLMs over Expanding Search Spaces](https://mlsanity.com/paper/2606.05464/) (2026)
- [Self-Play Search Distillation for Large Language Model Reasoning](https://mlsanity.com/paper/2609.30936/) (2026)

## Abstract (arXiv)

Large language models (LLMs) excel at many supervised tasks but often struggle with structured reasoning in unfamiliar settings. This discrepancy suggests that standard fine-tuning pipelines may instill narrow, domain-specific heuristics rather than fostering general-purpose thinking strategies. In this work, we propose a "play to learn" framework that fine-tunes LLMs through reinforcement learning on a suite of seven custom logic puzzles, each designed to cultivate distinct reasoning skills such as constraint propagation, spatial consistency, and symbolic deduction. Using a reinforcement learning setup with verifiable rewards, models receive binary feedback based on puzzle correctness, encouraging iterative, hypothesis-driven problem solving. We demonstrate that this training approach significantly improves out-of-distribution performance on a range of mathematical benchmarks, especially for mid-difficulty problems that require multi-step reasoning. Analyses across problem categories and difficulty levels reveal that puzzle training promotes transferable reasoning routines, strengthening algebraic manipulation, geometric inference, and combinatorial logic, while offering limited gains on rote or highly specialized tasks. These findings show that reinforcement learning over logic puzzles reshapes the internal reasoning of LLMs, enabling more robust and compositional generalization without relying on task-specific symbolic tools.