We aim to improve question answering (QA) by decomposing hard questions into simpler sub-questions that existing QA systems are capable of answering. Since labeling questions with decompositions is cumbersome, we take an unsupervised approach to produce sub-questions, also enabling us to leverage millions of questions from the internet. Specifically, we propose an algorithm for One-to-N Unsupervised Sequence transduction (ONUS) that learns to map one hard, multi-hop question to many simpler, single-hop sub-questions. We answer sub-questions with an off-the-shelf QA model and give the resulting answers to a recomposition model that combines them into a final answer. We show large QA improvements on HotpotQA over a strong baseline on the original, out-of-domain, and multi-hop dev sets. ONUS automatically learns to decompose different kinds of questions, while matching the utility of supervised and heuristic decomposition methods for QA and exceeding those methods in fluency. Qualitatively, we find that using sub-questions is promising for shedding light on why a QA system makes a prediction.