Mathematical noodling helps keep my aging brain sharp via mental exercise, and I get a sense of accomplishment and closure from renewing skills I attempted to master 50 years ago and have long since let fall by the wayside.
Each exploration is on a separate sub-page of this page. I cheat a lot and try to see how others deal with the problem (the only way a minor talent with a lazy brain can advance at all). Then I integrate the available information into a custom solution that clarifies the major points to me.
Note to students surfing the web to find answers to assigned problem sets: best not to copy my stuff; I am terrible at math.