Multiple factors of task difficulty keep problem solvers from finding the crucial thinking steps required to solve insight problems. In this study, we distinguished two difficulty factors, chunk familiarity and chunk tightness, and investigated their effects on chunk decomposition—a specific type of insight that depends on the process of breaking up perceptual patterns or chunks into elements so that they can be reorganized to form a new meaning. Subjects solved problems that required decomposing Chinese characters that differed in chunk familiarity and chunk tightness. Brain activity was recorded using the electroencephalogram and functional magnetic resonance imaging. The results showed that chunk familiarity could be overcome through an inhibition of familiar meanings, whereas overcoming chunk tightness required visual-spatial processing. Furthermore, chunk familiarity posed an additional difficulty when chunk tightness was high. This result demonstrates that the difficulty sources in a problem do not always simply add up. Rather, the difficulty of a problem can reside in the interaction of particular sources of difficulty. Hum Brain Mapp, 2013. © 2012 Wiley Periodicals, Inc.