Enigmata: Scaling Logical Reasoning in Large Language Models with
  Synthetic Verifiable Puzzles
Authors: name: Jiangjie Chen, name: Qianyu He, name: Siyu Yuan, name: Aili Chen, name: Zhicheng Cai, name: Weinan Dai, name: Hongli Yu, name: Qiying Yu, name: Xuefeng Li, name: Jiaze Chen, name: Hao Zhou, name: Mingxuan Wang

Large Language Models (LLMs), such as OpenAI's o1 and DeepSeek's R1, excel at
advanced reasoning tasks like math and coding via Reinforcement Learning with
Verifiable Rewards (RLVR), but still struggle with puzzles solvable by humans
without domain knowledge. We introduce Enigmata, the first comprehensive suite
tailored for improving LLMs with puzzle reasoning skills. It includes 36 tasks
across seven categories, each with 1) a generator that produces unlimited
examples with controllable difficulty and 2) a rule-based verifier for
automatic evaluation. This generator-verifier design supports scalable,
multi-task RL training, fine-grained analysis, and seamless RLVR integration.
We further propose Enigmata-Eval, a rigorous benchmark, and develop optimized
multi-task RLVR strategies. Our trained model, Qwen2.5-32B-Enigmata,
consistently surpasses o3-mini-high and o1 on the puzzle reasoning benchmarks
like Enigmata-Eval, ARC-AGI (32.8%), and ARC-AGI 2 (0.6%). It also generalizes
well to out-of-domain puzzle benchmarks and mathematical reasoning, with little
multi-tasking trade-off. When trained on larger models like Seed1.5-Thinking
(20B activated parameters and 200B total parameters), puzzle data from Enigmata
further boosts SoTA performance on advanced math and STEM reasoning tasks such
as AIME (2024-2025), BeyondAIME and GPQA (Diamond), showing nice generalization
benefits of Enigmata. This work offers a unified, controllable framework for
advancing logical reasoning in LLMs. Resources of this work can be found at
https://seed-enigmata.github.io.