You wont like my answer and you won't accept it because it steps outside of the assumptions of the P NP questions. = I made a writeup on the idea March 8th, 2014 that's long winded but I'll summarize: a) You have to break the rules. That's the 1st step. = That's the pattern to solve it. Treat situations on a case-by-case basis and involve real people. The problem comes from it being in the realm of thought experiments and looking for a Universal solution. But we *have* the universal solution: We use it every day. == We utilize it daily. We don't have a choice. We live amongst complexity, utilize complex systems in our minds and in our relationships with people and information. We navigate socially and introspectively alike. We ask other people when we're stuck (or force it out of them), and sometimes the answer is simply, "I don't know". or "I don't care" - which are valid solutions to problems, if unsatisfactory. For example: Want to crack a high-encryption NSA code? Look at the situation. Find the key players. Kidnap their family. Threaten them with death 'til they give you the passwords and SALT required. Its a solution. A professor from college sent me a magazine clipping - I still have it - about a $100,000 prize for solving Minesweeper about 15-18 yrs ago. He put an encouraging sticky note on it: "If anybody can do this, you can". I have no idea why he thought that. I put it aside 'cause I knew the answers even then and it's not the kind of answers they wanted. == The answer is sideways: Past the person playing, and behind the game board but in front of the CPU: sniff the instruction set and output it so the information skips PAST the game board and into the eyes of the person playing. That's how you solve it. == Every puzzle can be analogized to a maze. Thought experiments, logic experiments, mathematical puzzles, they're mazes. The moment you remember you're a person in a chair solving this problem and that this problem can have solutions OUTSIDE of the context desired by the puzzle-maker, your solution set opens up VERY VERY wide. You can go down the maze as requested, you can go around the maze, you can fold the paper so the START and END of the maze is touching, and skip time/space entirely. You can ask your friend to help you. You can find the answer online. You can solve it by not caring anymore about it and that's just a few. == Another way to solve it: Change the math. Newton did it. This new Japanese guy apparently solved a problem by inventing a new math but I bet I know what makes his new math work: He's creating a NEW LAYER of abstraction on top of the existing system. This new layer of abstraction gives him the flexibility to make connections that are impossible in current mathematics. This is the kind of solution I'm talking about. This is how you'd solve N NP, Minesweeper etc if the current methods aren't working. Go up a level. Step outside of the system you're using. == Anyway, these aren't the kinds of answers they want for the P NP problem. I solved the Travelling Salesman problem by making a 3D mockup of it and sticking a rubber-band around it so the elasticity of the rubber-band gave me the shortest path all at once. Sometimes the answers are so simple but when people expect complexity, that's what they look for and create. ==