Behavioural flexibility, the ability of animals to modify behaviours in response to novel challenges, is thought to be a key determinant in the persistence of some species within the expanding urban landscape. Behavioural flexibility is often tested using food-motivated problem-solving tasks, and inter-individual variation exists in the capacity to solve problems. We investigated the influence of inherent individual characteristics (personality and physiological stress), and behaviours involved in the problem solving process (flexibility rate, behavioural variety, functional manipulation, and learning) on problem solving abilities within an urban population of common brushtail possums (Trichosurus vulpecula). We validated the use of a corticosterone enzyme immuno-assay on brushtail possums and quantified the personality traits of boldness, activity, and exploration. We found that although aspects of the stress response correlated with measures of personality, stress reactivity, but not personality, influenced problem solving. This influence was manifest via proximate behavioural mechanisms. Moreover, increased problem-solving efficiency over trials indicated that possums are capable of combining simple associative learning with some scope for higher order cognition to exploit novel food resources. We suggest that behavioural flexibility may confer fitness consequences within the urban landscape, allowing possums to exploit novel resource opportunities.