Many scientific discoveries have been explained by a sudden gaining of insight with regards to an ongoing problem. Insight is characterised by a mental restructuring of acquired information, from which new explicit knowledge can be drawn, leading to qualitative changes in behaviour. Extended sleep facilitates the gaining of insight, possibly because it is conducive to the stabilisation and restructuring of new memory representations via consolidation. Research shows that a brief period of awake quiescence (quiet resting), too, can support consolidation: people remember more new memories if they quietly rest for several minutes after encoding than if they engage in a task involving ongoing sensory input after encoding. However, it remains unknown whether awake quiescence inspires insight. Using a number-based problem-solving task (the Number Reduction Task – ‘NRT’), we reveal that, like sleep, awake quiescence facilitates the rapid gaining of insight: young adults were more than twice as likely to demonstrate new explicit knowledge of a hidden solution to the NRT if initial exposure to this task was followed by 10 min of awake quiescence than an unrelated perceptual task. These findings indicate that, at least for the NRT, the development of insight is not restricted to sleep but can be achieved via a brief period of awake quiescence. Thus, contrary to conventional wisdom and theories, when faced with a novel problem we may not always need to ‘sleep on it’ to find a novel solution, simply ‘resting on it’ may be enough.