rack your brains
make a great effort to think of or remember something.
A rack was a medieval instrument of torture consisting of a frame on which a victim was stretched by turning rollers to which their wrists and ankles were tied.
To rack someone was to torture them on this device and the image in this idiom is of subjecting one's brains to a similar ordeal in the effort to remember something.
1998 – Spectator - If I rack my brains for something nice to say about our weather, I suppose it does at least enable us to grow better grass than they do in California.
Related Idioms and Phrases :
have something on the brain
be obsessed with something – informal
pick someone's brains
question someone who is better informed about a subject than yourself in order to obtain information - informal
rack your brains :
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