Teaching LLMs String Matching, Backtracking, and Error Recovery to Deduce Bases and Truth Tables for the Combinatorially Exploding Bit Manipulation Puzzles

This paper introduces a novel approach to solving bit manipulation puzzles for the NVIDIA Nemotron Model Reasoning Challenge, addressing the limitations of Large Language Models (LLMs) in logical rule deduction. Key innovations include reframing logic-gate deduction as a base-selection task using string similarity, implementing backtracking and error recovery mechanisms, and employing bit tokenization with interactive reasoning to enhance model performance. The proposed method achieved over 96% validation accuracy, marking the highest performance in its category and demonstrating significant advancements for practitioners dealing with combinatorial logic challenges in AI.