To rack one's brains
As a Chinese idiom, Pinyin is d ā NJ ī NGJ í L ǜ, which means exerting wisdom and energy. It's from reading in Hanlin Academy.
The origin of Idioms
Zhang Juzheng of the Ming Dynasty wrote in the book of reading in the Hanlin Academy: "it's not wise for the sage to do it with all his might to train the emperor."
Analysis of Idioms
A close synonym: to think deeply
Idiom usage
Used as a predicate or object; used for thinking
To rack one's brains
be washed by rain and blown by wind - yǔ mù fēng cān
gloomy eyebrows and wrinkled forehead -- knit the brows - chóu méi cù é
yield twice the result with half the effort - shì bàn gōng bǎi
have the courage to take the blame for what one does - gǎn zuò gǎn dāng