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rack one's brain(s)
Fig. to try very hard to think of something. I racked my brains all afternoon, but couldn't remember where I put the book. Don't waste any more time racking your brain. Go borrow the book from the library.
rack your brain/brains
to think very hard, usually in order to remember something or to find a solution to a problem I've been racking my brains but I still can't remember who wrote that play.See go to rack and ruin
rack (one's) brainInformal
To think long and hard: I racked my brain for hours trying to recall her name.