Deep Learning vs Puzzle Games

You're bored on your phone and have some time to kill, so you decide -- against your better judgement -- to visit the games section of the app store to see what's trending. You see a puzzle app that looks fun, but it doesn't really matter, because you're only going to play this for half an hour then delete it and forget about it, right? The premise of the game -- one of the most popular mobile games on both iOS and Android since its 2012 release -- is stupidly simple: connect "valves" of different colours on a 2D grid, without 2 lines ever crossing: The level in the screenshot may seem simple, but it does get harder. As the levels progressed, I found myself coming up with some tactics that would help me solve these advanced levels faster (e.g. This begged the question -- could a computer, not through brute force but through "experience", learn these techniques as well?