What is "to rack one's brains out"

Rack \Rack\ (r[a^]k), v. t.

1. To extend by the application of force; to stretch or strain; specifically, to stretch on the rack or wheel; to torture by an engine which strains the limbs and pulls the joints.

   He was racked and miserably tormented.
   --Foxe.

2. To torment; to torture; to affect with extreme pain or anguish.

   Vaunting aloud but racked with deep despair.
   --Milton.

3. To stretch or strain, in a figurative sense; hence, to harass, or oppress by extortion.

   The landlords there shamefully rack their tenants.
   --Spenser.

   They [landlords] rack their rents an ace too high.
   --Gascoigne.

   Grant that I may never rack a Scripture simile beyond the true intent thereof.
   --Fuller.

   Try what my credit can in Venice do; That shall be racked even to the uttermost.
   --Shak.

4. (Mining) To wash on a rack, as metals or ore.

5. (Naut.) To bind together, as two ropes, with cross turns of yarn, marline, etc.

   To rack one's brains or To rack one's brains out or To rack one's wits, to exert one's thinking processes to the utmost for the purpose of accomplishing something; as, I racked my brains out trying to find a way to solve the problem.

   Syn: To torture; torment; rend; tear.