verb

• (intransitive) To investigate something, or solve a problem using brainstorming.
  "Meanwihle at Winterfell, another overdone scheme designed mainly to surprise the audience. In the black of her chambers, Sansa brainstorms with Littlefinger what Arya could want. “After she murders you, what does she become?” he asks. To which Sansa does everything but gasp and spit-take, widening her eyes and saying like she’s just realizing it for the first time, “Lady of Winterfell.”"
• (intransitive) To participate in a brainstorming session.
• (transitive) To think up (ideas); especially, to do so creatively.
  "I need you to brainstorm some suggestions for next week's activity schedule."

noun

• (US) A sudden thought, particularly one that solves a long-standing problem.
  "I had been working on the problem for weeks, and then I had a brainstorm and saw that the solution was easy."
• (British) An unexpected mental error.
  "2005 October 5, "Iguchi hit ruins Red Sox's night", BBC Online, 5 October A terrible fielding error from Tony Graffanino proved costly. … Aaron Rowand collected an RBI double to get them off the mark before Graffanino's brainstorm. Juan Uribe hit a roller to the second baseman, who let the potential inning-ending double-play ball roll under his glove, leaving runners at first and third bases."