Many important problems require consideration of multiple constraints, such as choosing a job based on salary, location, and responsibilities. We used the Remote Associates Test to study how people solve such multiply-constrained problems by asking participants to make guesses as they came to mind. We evaluated how people generated these guesses by using Latent Semantic Analysis to measure the similarity between the guesses, cues, and answers. We found that people use two systematic strategies to solve multiply-constrained problems: (a) people produce guesses primarily on the basis of just one of the three cues at a time; and (b) people adopt a local search strategy--they make new guesses based in part on their previous guesses. These results inform how people combine constraints to search through and retrieve semantic information from memory. (Contains 5 figures.)