Individuals encounter problems daily wherein varying numbers of constraints require delimitation of memory to target goal-satisfying information. Multiply-constrained problems, such as compound remote associates, are commonly used to study this type of problem solving. Since their development, multiply-constrained problems have been theoretically and empirically related to creative thinking, analytical problem solving, insight problem solving, intelligence, and a multitude of other cognitive abilities. Critically, in order to correctly solve a multiply-constrained problem the solver must have the solution available in memory and be able to target and access to that information. Experiment 1 determined that the cue – target relationship affects the likelihood that a problem is solved. Moreover, Experiment 2 identified that the association between cues and targets predicted inter- & intra-individual differences in multiply-constrained problem solving. Lastly, Experiment 3 found monetary incentives failed to improve problem solving performance likely due to knowledge serving as a limiting factor on performance. Additionally, problem solvers were shown to be able to reliably assess the likelihood they would solve a problem. Taken together all three studies demonstrated the importance of knowledge & knowledge structures on problem solving performance.