Everyone, I believe, the beginner will have a solid way to identify oportunities.
The advanced will start to see these geometric patterns, anyways I hope.
There are more patterns to be found, these that I call TIC-TAC-DOT patterns.
As soon as I figure how to put them on the web, I will do so.
This much I can say.
For the person that learns the frequency of TTD patterns. There will be no guessing without the knowledge of certainty. Not a computer, but a real brain.
We'll see who will take the DOTTIN paterns to it's final place in sudoku lore.
TIC-TAC-DOT patterns are next..
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I also came upon the same dot-based technique independently and have been able to solve the most horrendously difficult puzzles using it. The reason it works is that it inherently accounts for all the valid and invalid possibilities for a given number in a cell. What's required to make the system understandable and maximally powerful is a procedural step-by-step description including 1) how to mark cells within a grid 2) how to use the markings in sets of cells within a grid to refine the markings of other cells within the same grid and by extension to 3) refine the markings of cells in related rows and columns outside a given grid and 4) to apply more advanced pattern observation techniques to refine the markings within larger cell/grid groups. This last point (4) is the most important key to solving the most difficult puzzles. It includes not just locking pairs, but also triplets and, most impotantly, identifying inherent locks across large cell/row structures. Once these principles are systematically described and illustrated carefully (and graphically) using the simplest to the most complicated examples, it will become possible for anyone who thinks systematically to solve "any" sudoku puzzle. And once this level of competence is reached, the problem shifts from "how can this puzzle be solved" to "how can I solve this puzzle most efficiently", that is, what is the quickest solution. Ironically, this is where creativity actually comes into play in Sudoku. I say "ironically" because by nature soduko does not offer anything at all creative as to the end result - unlike with chess, checkers, most sporting events and life in general, where the outcome is not predictable, by definition, there is only one solution in a given sudoku puzzle, so what's left to creativity is the approach, techique and procedural application, all which can also be described to the student systematically, but with a lesser degree of certainty as to their ability to save time in all cases. And that's where individual creativity comes into play. I hope I've said something of use here.
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