Green’s Dictionary of Slang

1. to think, to brainstorm.

1945

‘Campus Sl. at Minnesota’ in AS XX:3 Oct. 233/2: Despite the distraction, Ann and I finally got down to work and really noodled for about an hour.

2. usu. constructed as noodle out/up, to mull something over, to work something out.

1955		‘Blackie’ Audett Rap Sheet 42: Scotty Lawrence had noodled out the general way we would have to take and had men spotting all the ranches in the district. [Ibid.] 143: They got hold of me and asked me did I have anything noodled up for getting away.
1998		L. Stringer Grand Central Winter (1999) 106: After three oblique and muddled drafts, I finally noodle out the essence of the story.
2002		J. Franzen Corrections 347: Brian spent his executive afternoons noodling around with computer code and Fourier analysis.
2016		V. McDermid Out of Bounds (2017) 438: Noodling around with motive wasn’t taking her any closer to finding [...] evidence.