>your conscious executor is simply way way way too stupid to handle this depth of problem by reasoning it out, you have to offload 95% of the processing off to your subconscious before you can actually program

There's a lot of truth to that. Whenever I encounter a problem I can't easily figure out, I take a brisk walk and give my subconscious a chance to tackle it. If that's not enough, I then have to pull out my (so far) foolproof heavy-hitter: a good night's sleep.