TTD's at work

In this example I will show you how a TTDs can help you to solve a puzzle




Look at the numbers five, there are five written on the grids.
The other four grids have the POP's (points of possibilities) dotted in. I have circled those in red.

I performed a TTD on the number five (incomplete of course) as seen below

Below it I have done a pair of DDTs with the POPs (and yes RW sometimes you'll need a fourth dot in this process)
The grids without the number 5 are, left center and left bottom plus right center and right bottom.
By overlapping the POPs over the uncompleted TTD pattern, you will notice that the only possible pattern is the "airplane". (topside bottom left)
This knowledge will not solve the number 5 pattern, because there is two options for the completion of the said pattern. But.
You can eliminate (r6c2) and (r9c8) or as I like to simplify (6x2) and (9x8).

You can "logically" eliminate those two cells as candidates for the number 5.
Thereby cell (6x2) becomes a possible 1-8 and cell (9x8) becomes a solved 9.
All this was accomplished through the use of deductive TTDs.

PATTERNS

The benefits of knowing TTD's?

This is a very interesting question, I'd thought about it.
I then realized, that as far as solving puzzles I have honestly used them a few times successsfully. Having said that.
I have used them in the process of trying to get past the typical hump of the good puzzles, many a times.
I am talking about the one place in the solving process where you find yourself with not enough information to continue along by the use of pure logic.
Meanwhile, I have often been able to correct myself by using TTD's, methodically.
I have also been able to make some pretty good guesses by the use of TDD's.
I feel the presence of esoteric knowledge in here, and yet, not quite able to give you a full description, let's just say that more research is needed.
My hope is that the fractal like elements of the sudoku could someday be understood.
And once the combination of patterns are deciphered, and the numbers of such combination are cataloged. These patterns could become a graphic language of the grids and these could very easily aid you to recognize the individual characteristics of the different sudoku programmers out there.
Seeing the puzzle from a different angle will also expand your understanding, however subtle that may be.
The question to you is this..
Can you think in dots at your present state of knowledge?
The answer is, most likely not.
You have to solve many a puzzles, first, to acquire some proficiency. And accuracy.
This process will tune your mind to the world of POP's.

Examples of patterns

Each of the 1's inside the nine grids, has a position within the grid.

So you mark those positions as dots on your criss-cross pattern.

Begin with the first grid in the upper left, and end, on the ninth grid at the lower right of the puzzle. The resulting pattern is this.

(you will always have a total of 9 dots to work with)

In this example we will use the number 1

notice how the second time a dot a applied, it is actually a circle around the first dot

The next pattern will be performed by using the number 6

I call this one the bomb, notice the third instance of a dot, it becomes a large black circle

Next is example A:

Using the number 4

What is a TIC-TAC-DOT pattern ?

To explain this matter one must understand that the patterns have always been there.
What I have developed is a "way" to expose them, and a manner in which, to make these available for further scrutiny. By everyone.
The theorem goes as such:

" Each number creates a pattern on the grid "

And to reveal the pattern I have overlapped the positions of the number into a single window. For everyone to see.

How I go about this process, is quite simple. Really.
This is what you have to do.

1. Draw out a pair of crossing paralell lines (just like the ones for tic-tac-toe).


2. Mark the position of the selected number within the nine grids of the puzzle. By placing a corresponding dot within the crossed lines, exactly as you see them positioned in the grids.


3. And.. voila, youve got it. That is, you should be able to "see" a recognizable pattern.

Now, you will have instances in which the dots will overlap each other. And for that ocasion I have developed a systematic order for dots to be applied. (see the pictures).