绞尽脑汁

Explanation: Racking their brains. 　　Usage: Verb-object type; as the predicate attribute, object, adverbial; means exhausted their brains 　　Source: Lao She, "Four Generations in drag on" thirty-seven: "Only in this way, he can be able to show the way their brains, for she thought." 　　Examples: Encounter this problem, he could not think of a solution ~ to. Thesaurus:  Pakistan, after the former operator, ponder over, contemplate, think from different angles, cudgel one's `brains think very hard