So, to solve a maze on paper I've decided to make a series of images and describe all the techniques I use in solving this kind of maze. So, we'll try a smaller maze for the sake of ease, but the techniques I show you will apply to bigger mazes as well. Note that what works for mazes like this one will take a little bit of "translation" to work on one of my squiggly mazes. You're on your own with those :p
Without further ado, here is the maze we'll be working on:
Now, we'll start from the top.
Just go until you come to a split in the road. The idea is every time the path splits, you look down both paths and choose the one that doesn't dead end shortly. The first few branches are ridiculously short, so it's pretty obvious to skip them. Look at where I stopped. There's a path going down on the right and one on the left. The right path boxes itself in. This is a pattern you should look for. Think of it as a box of death. You don't actually have to look at the path, so much as the wall surrounding the box. I'll highlight that in the next picture and move down the the first real branch.
Notice the box I drew around the dead end we discussed earlier. When solving mazes, people focus a lot on the path, scanning it quickly to find dead ends. You may find your eyes getting lost doing this. There are situations where looking at the actual WALL can be more helpful, as in this case. It's a small box and it's pretty obvious it's a dead end, but you'll find that this applies to some pretty big boxes as well.
Moving on, I've drawn my path up to the first major junction in the whole maze. Mark this (with a circle or whatever you want), and then choose a direction. Now, I already know which way to go, and frankly this maze turned out to be way too easy (it was computer generated). So I'm going to intentionally go the wrong way to show you folks a couple more things.
So, I've just wandered off in a completely wrong direction. Whatever, I know where to go back to if (when) this way doesn't work out. As you can see I've marked another junction, and chosen a direction from there. Now your attention has probably been focused on the big red thing. The path down from where I stopped is just full of dead ends. When you see something like this while your solving, just wall it off yourself. You don't want to waste your time looking at that later on. The red area is another example of a box of death. Check out the walls. There is an unbroken wall from your path to your path again. That means there is no way out.
Turns out, my other option from there dead ends too, so I'll just go back to the last junction I marked.
I've worked my way to another junction. Don't waste your time following the paths with your eyes here. When you're this close to the boundary of the maze you can look for a "crack" in the maze. Notice the blue wall I highlighted. Clearly, the path on the right won't get me anywhere.
I moved up to another little junction. See that path with the arrow? Following that path with your eyes, you can tell it won't go anywhere as soon as it gets to where that blue X is. Seeing that you would just take the right path down from the junction you stopped at and continue on. Eventually, however, you would realize that you can't reach the exit from the paths you've taken. When that happens you just go back one junction at a time, exploring all possible paths out. However I've already ruled out every option on the last junction I have marked, so that leaves me with the first one.
From the first junction I just work my way down, using all the techniques to find my way to the exit. Piece of cake! I should mention, most of the things I've drawn are just to illustrate techniques that you do in your head. You should mark important junctions, and if you find it helpful block off bigger dead end paths you notice, but you don't have to draw all over everything.
So there you go. Good luck solving mazes and have fun :]
