Sampling complete solutions gives large language models (LLMs) more chances to solve a problem, but each attempt restarts from scratch. For tasks composed of several subproblems, all required answers must be correct within the same attempt. Retaining intermediate results can avoid repeating correct work, yet errors in those results may corrupt later steps. We investigate when such reuse is reliable and how much computation it entails. For local retries that stop once no candidate passes within the retry budget, we provide sufficient conditions for correct completion and bound the average number of attempts. We also analyze how checking cost and the probability of passing a check jointly affect total computation. Experiments span eight reasoning models on composite mathematics and arithmetic. Using four DeepSeek models, the average success on the second subproblem is 36.2% without any first‑subproblem context, 57.2% when only the answer is provided, and 58.3% when both the reasoning process and answer are supplied. These scores measure second‑subproblem coverage and include continuations when selection fails. Arithmetic experiments show that similar first‑attempt accuracies can lead to very different coverage after repeated attempts. Code is available at https://github.com/SempraETY/Intermediate-State-Reuse
Review: The paper offers a clear theoretical framework and empirical evidence on the limits of intermediate‑state reuse, giving practitioners concrete criteria for building more efficient LLM reasoning pipelines.