Puzzle out
Definition 1 of 1
Pro Tip 1/3Complex problems
Use 'puzzle out' when referring to solving something that is not straightforward or has many parts. 
It took me hours to puzzle out the assembly instructions for the new desk.
Pro Tip 2/3Mental effort
'Puzzle out' indicates you used careful thought or consideration to understand something. 
She puzzled out the cryptic message left on her desk.
Pro Tip 3/3No direct clues
Use it when there are no clear answers and you have to deduce the solution yourself. 
The detective had to puzzle out the suspect's motive with little evidence.