verb, "to noodle" - means to mull over, think about, contemplate, ponder, puzzle over or brain-storm.
1) "Jack, do we have a way to make gold from salt-water, yet?" "I don't think so, Bob. Let me noodle that one for a bit. I'll get back to you!"
2) Christy was struggling with her Powerpoint presentation, so she decided to take a break and noodle it.
3) The physics students were always noodling over one or another silly idea.