To problems that can't be solved (like how can I get my wife back) I just imagine I have solved it, or my brain will just keep trying to solve the problem. For solvable problems i either brute force by moving the mountain one sand corn at at time, or keep iterating. When you have a grip on how much the problem will cost to solve you have to ask yourself it it's worth solving - or if you can just use a more crude existing solution.