rack one's brains：绞尽脑汁

动词rack有“将人绑到架子上折磨”之义，进一步泛义为“使痛苦不堪、使受折磨”。

rack your brains是“绞尽你的脑汁、冥思苦想”，如

【例句1】She began to rack her brains to remember what had happened at the nursing home. （她开始冥思苦想回忆起疗养院发生的事情。）[柯林斯高级学者辞典]

【例句2】I racked my brains, trying to remember his name. （我绞尽脑汁，试图记住他的名字。 ）[朗文当代英语词典]

【例句3】I've been racking my brains all day but I can't remember her name. （我整天都在绞想方设法，但我记不起她的名字了。) [剑桥高级学者辞典]

【例句4】She racked her brains, trying to remember exactly what she had said. （她千方百计汁，试图准确地记住她说的话。）[牛津高级学者辞典]

【例句5】We racked our brains but we couldn't come up with a solution. （我们搜肠刮肚，但没能想出解决办法。 ）[牛津高级学者辞典]

注意brain是复数，这可能是因为该表达比较新，而按现代人体解剖学，每个人都有左脑右脑、大脑、小脑等。