The nature of novel idea creation in design depends on the nature of the design challenge: how requirements and constraints not only determine what is acceptable but also shape thinking. This paper explores how overconstrained and underconstrained problems are tackled in fundamentally different ways, using engineering design, knitwear design and software development as exemplars. Problem framing as well as the iterative reformulation of the design problem is crucial in all fields but is done very differently. However, designers face a variety of problem types, including problems resembling those typical in other industries; this paper argues that a wider awareness of the creative thinking methods used in other industries would aid designers in many fields to tackle unfamiliar problems.