To illustrate, I show how I go about solving a maze.
I paste a screen grab into a raster editor and work on it there.
A brute-force approach is to pretend to put a left or right hand on the wall and walk to the solution. But what fun is that?
Instead, I examine possible paths and block off dead ends.
By not playing on the puzzle site, I can approach the problem from both the start and the finish, much like “cheating” when deriving an equation in math or science class. Such is the case with this maze.
This branch is complicated, but not so much that I cannot determine in my head that it is a dead end.
If a branch is too complex to complicated to do in my head, I analyze sub branches off of that branch; if the entire branch proves to be a dead end, I use UNDO to remove the extraneous yellow marks.
When the puzzle is solved, I use flood fill to color in the dead ends, leaving a clear path to follow on the puzzle site.
I find this approach both challenging and entertaining enough to pursue.