Although problem-solving tasks are frequently used to assess innovative ability, the extent to which problem-solving performance reflects variation in cognitive skills has been rarely formally investigated. Using wild breeding great tits facing a new non-food motivated problem-solving task, we investigated the role of associative learning in finding the solution, compared to multiple other non-cognitive factors. We first examined the role of accuracy (the proportion of contacts made with the opening part of a string-pulling task), neophobia, exploration, activity, age, sex, body condition and participation time on the ability to solve the task. To highlight the effect of associative learning, we then compared accuracy between solvers and non-solvers, before and after the first cue to the solution (i.e., the first time they pulled the string opening the door). We finally compared accuracy over consecutive entrances for solvers. Using 884 observations from 788 great tits tested from 2010 to 2015, we showed that, prior to initial successful entrance, solvers were more accurate and more explorative than non-solvers, and that females were more likely to solve the task than males. The accuracy of solvers, but not of non-solvers, increased significantly after they had the opportunity to associate string pulling with the movement of the door, giving them a first cue to the task solution. The accuracy of solvers also increased over successive entrances. Our results demonstrate that variations in problem-solving performance primarily reflect inherent individual differences in associative learning, and are also to a lesser extent shaped by sex and exploratory behaviour.