Same Task, Different Statement: When and How Reformulation Helps LLM Problem Solving

When people face a hard problem, they often restate it in a clearer way before solving it. We study whether the same habit helps large language models by rewriting the statement of a problem. A legal rewrite must keep the meaning, the constraints, and the correct answer unchanged. We test three kinds of rewrites. Decomposition makes hidden subgoals explicit. Typed Reformulation casts the task into a more suitable solving frame. Concept Reduction removes surface detail and exposes the task structure. We evaluate them on eight math, logic, and code benchmarks with eight models, all under the same chain-of-thought solving prompt. The effect is large but depends on the problem type. An oracle that picks the best rewrite after the fact raises accuracy by +27.6% on average. Yet no single rewrite helps every problem, and a mismatched rewrite can hurt. Still, the effect follows clear patterns. Each kind of rewrite fits certain problem types. A simple fixed rule learned from one set of problems transfers part of the gain to new problems. It gains +11.0% on the problems it chooses to rewrite, while blind rewriting loses 5.6% on a similar share of problems. Rewriting is therefore not a universal way to solve problems. The question is when and how to rewrite.