The New Sudoku Players' Forum

[Mauriès Robert]

The TDP ("Technique des pistes" in French) is a network technique, as there are others (GEM, Medusa3D etc...)
I developed this way of solving in 2011 using only the basic techniques so that it is easy to use for sudokists with little experience in advanced techniques. But I also wanted to give it a rigorous theoretical framework, which is why I call it TDP Theory.
You will find the PDF document in English with this link : https://www.assistant-sudoku.com/Pdf/TDP-anglais.pdf
This is a simplified version of the full document (in French) that you will find with this link : https://www.assistant-sudoku.com/Pdf/theorie-des-pistes.pdf

You will also find on the internet my website (in French) dedicated to sudoku with this link: https://www.assistant-sudoku.com/

Robert Mauriès

[smcroberts]

This is fascinating, Robert!
I found the English document too hard to follow (not being an academic), so I took a stab at translating your simplified version from French to English (primarily via Google Translate), and am just starting to read through it. I will attach the translation in another reply, if you will permit me.

[Mauriès Robert]

Hi smroberts,

This is fascinating, Robert!
I found the English document too hard to follow (not being an academic), so I took a stab at translating your simplified version from French to English (primarily via Google Translate), and am just starting to read through it. I will attach the translation in another reply, if you will permit me.

There are several documents in French, which one do you plan to translate?
Having said that, I am working on improving the English document, of which I will also make a French version, because it does not deal with the puzzle of multiple solutions.
I remain at your disposal to talk about TDP.
Robert

[smcroberts]

Hi Robert,

The document I attempted to translate is:

This is a simplified version of the full document (in French) that you will find with this link : https://www.assistant-sudoku.com/Pdf/th ... pistes.pdf

I had trouble understanding the non-simplified English version document as it started out rather cryptically with notation I was unfamiliar with. But the simplified version is a good introduction.

Here is a very high level summary of what I think you are saying (please correct me if I'm wrong):

1. Choose a candidate (A) from a bi-value cell or conjugate pair.
2. Assume A is true, and color it blue.
3. Look over the board for candidates that are forced to be true due to the blue candidate(s) being true. Color these blue as well.
4. Repeat step 3 using the new blue candidates until no more are found or a contradiction is discovered.

5. Choose the candidate that pairs with A (e.g. the other candidate of the bi-value cell that A lives in) call this B.
6. Assume that B is true, and color it yellow.
7. Look over the board for candidates that are forced to be true due to the yellow candidate(s) being true. Color these yellow as well.
8. Repeat step 7 using the new yellow candidates until no more are found or a contradiction is discovered.

9. If a track would result in a contradiction, the initial assumption is false. e.g. if A results in a contradiction, A is false and can be eliminated, which makes B true, along with all yellow candidates!

Assuming no contradiction was found:
10. Any uncolored candidate that sees its match in both blue and yellow can be eliminated.
11. Any candidate colored both blue and yellow is the solution for its cell!

Repeat, starting with step 1 (and a new pair) until the puzzle is solved.

[Mauriès Robert]

Hi smcroberts,
Indeed, the method can be summarized in the 11 steps you describe. But TDP does not stop there, especially with the notions of anti-track and extension.
The English version of TDP will be a good complement to what you have understood.
You will find in part 2 the elements you have described, and in part 1 the anti-tracks.
Also, I give some solutions to the tarek and eleven puzzles on this forum, go check it out, or with the puzzles I propose (Robert's Puzzles), for example : http://forum.enjoysudoku.com/post286356.html#p286356 and http://forum.enjoysudoku.com/post286389.html#p286389
Robert