An individual encounters problem of varying difficulty every day. Each problem may include a different number of constraints. Multiply-constrained problems, such as the compound remote associates, are commonly used to study problem solving. Since their development, multiply-constrained problems have been related to creativity and insight. Moreover, research has investigated the cognitive abilities underlying problem solving abilities. In the present study we sought to fully evaluate a range of cognitive abilities (i.e., working memory, attention control, episodic and semantic memory, and fluid and crystallized intelligence) previously associated with multiply-constrained problem solving. Additionally, we sought to determine whether problem solving ability and strategies (analytical or insightful) were task specific or domain general through the use of novel problem solving tasks (TriBond and Location Bond). Multiply-constrained problem solving abilities were shown to be domain general, solutions derived through insightful strategies were more often correct than those derived through analytical strategies, and crystallized intelligence was the only cognitive ability that provided unique predictive value after accounting for all other abilities.