In the authors' attempts to incorporate problem solving into their mathematics courses, they have found that student ambition and creativity are often hampered by feelings of risk, as many students are conditioned to value a produced solution over the actual process of building one. Eliminating risk is neither possible nor desired. The challenge, then, is to understand and help students manage the risks associated with creative mathematical work. The authors present here a structure for short-term work that maintains the coherence of the problem-solving process, places emphasis on the process rather than the produced solution, and creates an artifact of that process for further reflection and discussion. The structure is based on the quickfire challenge that is common and popular on competitive cooking and design shows. In this article, the authors explain what they mean by "quickfire challenge," describe one quickfire challenge that they have incorporated into their instruction, and share how their classroom norms influence its use. They conclude by brainstorming ways to use the student reasoning and products produced in a mathematical quickfire challenge to inform instruction and make decisions about future activity.