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cudgel (one's) brains
To try very hard to comprehend, solve, think of, or remember something. I was up all night cudgeling my brains for a way to pay off all my debts. She cudgeled her brains to remember the man's name.
take up arms (against someone or something)
to prepare to fight against someone or something. Everyone in the town took up arms against the enemy. They were all so angry that the leader convinced them to take up arms.
take up arms(slightly formal)
to fight with weapons against an enemy They took up arms only after other means of resolving their differences failed.
take up the cudgels for somebody/something(British & Australian) also take up the cudgels on behalf of somebody/something (British & Australian)
to argue strongly in support of someone or something
Usage notes: A cudgel is a short, heavy stick which is used as a weapon.Relatives have taken up the cudgels for two British women accused of murder. (British & Australian)
rack one's brain
Also, cudgel one's brains. Strain to remember or find a solution, as in I've been racking my brain trying to recall where we put the key, or He's been cudgeling his brains all day over this problem. The first term, first recorded in 1583 as rack one's wit, alludes to the rack that is an instrument of torture, on which the victim's body was stretched until the joints were broken. The variant, from the same period, uses cudgel in the sense of "beat with a cudgel" (a short thick stick). Shakespeare used it in Hamlet (5:1): "Cudgel thy brains no more about it, for your dull ass will not bend his pace with beating." Also see beat one's brains out.
take up arms
Also, take up the cudgels. Become involved in a conflict, either physical or verbal, as in The Kurds took up arms against the Iranians at least two centuries ago, or Some believe it's the vice-president's job to take up the cudgels for the president. The first term originated in the 1400s in the sense of going to war. The variant, alluding to cudgels as weapons, has been used figuratively since the mid-1600s and is probably obsolescent.
take up the cudgels
To join in a dispute, especially in defense of a participant.