Question asking is a key tool for learning about the world, especially in childhood. However, formulating good questions is challenging. In any given situation, many questions are possible but only few are informative. In the present work, we investigate two ways 5- to 10-year-olds and adults simplify the challenge of formulating questions: by reusing previous questions, and by remixing components of previous questions to form new questions. In Study 1, we develop a new question asking task, verify its suitability for studying question asking in children and adults, and conduct a preliminary investigation of how children and adults reuse and remix their own prior questions. In Study 2, we experimentally manipulate exposure to another person's questions, investigating under what conditions children and adults reuse and remix others' questions. Our experimental results suggest that both children and adults reuse and remix questions, and they adaptively modulate reuse depending on how informative a question will be in a particular situation. Moreover, children reuse prior questions more frequently than adults in some cases. This work shows that prior questions provide fodder for future questions, simplifying the challenge of inquiry and enabling effective learning.