How many ways to go?
In this case also you may enter through any opening and go out through any exit.
Only one restriction I still impose
- While on your way, you must not retrace your path.
Two different problems on this maze and two questions
- Entry and exit should be from opposite sides. How many ways? I have found 2 ways. Can you reach 2? Is there any more ways?
- Along how many paths can you walk in and out of the maze?
You may spend some time in forming more questions on the maze. As a hint, you may try the new problem,
- What is the shortest path in and out of the maze?
And then go on to solve it.
This is not the only additional problem you may form out of this maze though. Each time I saw a new problem in the maze, I felt a tinge of joy. To me there is always a joy associated with a discovery, however little or monstrous it might be.
Solving the maze is not so important, looking at the problem from all angles is more important.
If you look at a problem from all angles, and do this on various problems, many times, your ability to think new goes on increasing, and this ability is one of the more important problem solving skills.
I have another name for this problem solving skill enhancement techniquee - the many ways technique:
By nature, when I face a problem, not only do I look automatically at every aspect of the problem during the solving process, but even after its solution I try to find other paths to the solution.
In short, pacticing many ways technique has become my habit.
In a number of my more detailed problem solving posts here, I have mentioned this technique, but only one complete post is devoted to this very important problem solving skill enhancement technique. You may refer to it here.
The other skill that you use in any of the problems that you solve is the pattern recognition skill, and you use it by pattern recognition techniques.
Without ability to detect and use of effective patterns no problem can be solved.
To improve a useful pattern recognition skill, you need to solve problems that you learn to solve efficiently yourself by detecting useful patterns. The more you solve problems efficiently by identifying useful patterns, your pattern recognition skill gets stronger. After all, it's not a medicine that can be injected in you to increase your brainpower. You can and have to do it yourself, if you want. Without depending on any help from anyone.
If you have never solved any maze problem before seriously (unless you try to solve a problem with seriousness, not only do you tend to reach an inefficient solution, you also do not learn much from the efforts), you won't know how to solve a complex maze problem easily (barring exceptions) at the very start.
The method to build powerful skills in any area is to
Start solving simple problems in the area, learn from the solving process and add the learning to your problem solving concept and skill layer. When you are comfortable in solving problems at a certain difficulty level, move up one difficulty level and start solving more difficult problems. Thus improve your problem solving skill bit by bit, incrementally.
The last but one of the most crucial skills in reaching top rung skill levels in an area is System building skill,
The ability to bind the patterns and processes learned in solving earlier problems into usable rich concept systems. Without a strong Systems approach or skill in dealing with abstractions, this does not usually happen.
This is a more advanced skill and more exposure is needed to exploit this skill level fully.
In any case, just forget the theories and enjoy solving this maze. It's still simple.
And watch out for more surprises.