## Almost-binary puzzle

Advanced methods and approaches for solving Sudoku puzzles

### Re: Almost-binary puzzle

Hi totuan,

totuan wrote:Present as diagram: => r7c2<>7
diagram: Show
Code: Select all
`(7)r3c9-r1c7=r7c7* || ||      -(4=19)r23c7-(9=2)r5c7-r5c3=r6c3-------(7)r6c3 ||     |                                        ||  (4)r3c9--r3c2=r2c2-(5)r2c2                      (7)r6c2*   ||                 ||                           || ||                (5)r3c2-r3c6=r2c5-(5=7)r5c5--(7)r6c5 ||                 || ||                (5)r7c2*      || ||                         (5)r2c2-r2c5=r5c5---(7)r5c5 ||                          ||                  ||         ||       (4)r2c7-r2c2=r3c2—(5)r3c2             (7)r5c2*      ||        ||                ||                  || ||     --(9)r2c7           (5)r7c2*            (7)r5c3  ||    |   ||                                    | ||    |  (1)r2c7----------------------------    | ||    |                                     |   |  ||    |                                     |   |(9)r3c9--(7)r3c9=(7-8)r1c7=(8)r2c9-(8=1)r2c4-    |             |                                         |            -(9=14)r23c7-(4=2)r6c7-r6c3=r5c3---------`

Many thanks for that diagram! Very interesting. Hodoku can't find such nets, probably due to the multi-kraken nature, so examples of logic like that are hard to come by. It is, however, perfectly understandable in your neat notation. Now I'm just wondering how best to search for such beasts manually. Any tips? Seems kind of hard to keep track of all the branches.

Anyway, I chose to use that as a practice case to write my very first Block Triangular Matrix. Thanks to Cenoman and his help, I've learned to like matrices as a supporting notation for complex logic, but so far I've only used the basic Pigeonhole and Triangular Matrices. With so many kraken branches this seemed like a prime example to try the BTM variant, because I don't think it could be written as a basic TM.

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` BTM 21x21 (sub-TMs: 10x10 + 13x13)----------------------------------------------------------------------------------- 7r7c7 7r1c7       7r3c9 9r3c9 4r3c9                     4r3c2  4r2c2 5r7c2                    5r2c2 5r3c2                                 5r3c6 5r2c5                                      5r5c5 7r5c5                   4r23c7                         19r23c7                                                   9r5c7  2r5c7                                                          2r5c3  2r6c3 7r6c2                                      7r6c5                7r6c3                    ================================================================             7r3c9 7r1c7                   8r1c7  8r2c9                          8r2c4 1r2c4             9r2c7              1r2c7 4r2c7                                      4r2c2 4r3c2 5r7c2                                      5r3c2  5r2c2                                                   5r2c5  5r5c5             9r23c7                                             14r23c7                                                                 4r6c7  2r6c7                                                                        2r6c3 2r5c3 7r5c2                                                    7r5c5               7r5c3------------------------------------------------------------------------------------7r7c2`

I don't know if you're familiar with the concept, but if you are, would you agree that I captured your logic? I'm obviously using a slightly different approach from SteveK's by splitting the cases (4r3c9 and 9r3c9) vertically. Not only does it save horizontal space, but I think it's much more understandable with the two sub-matrices clearly separated.

Make no mistake, I'm not implying that matrices are somehow a better (or any) alternative to your diagrams! Not at all. Obviously the diagrams provide a much nicer and more intuitive view of the logic flow, so I definitely want those. Like I said, I see matrices as a supporting tool, not a presentation method.

SpAce

Posts: 2674
Joined: 22 May 2017

### Re: Almost-binary puzzle

Hi SpAce et Totuan,
Here, below, in the TDP way, is a diagram equivalent to that of Totuan.
These complex chains (nets) use what I call in TDP extensions (or bifurcations) at the 5c2(*) level.
Thus I recognize in the Totuan diagrams a great similarity with TDP.
Who is behind these diagrams?
Sincerely
Robert
Code: Select all
`P(7r3c9) : 7r3c9 -> 7r7c7 -> -7r7c2                 4r9c8 -> 4r6c7 -> 2r5c7 -> 2r6c3                |              |                |P(4r3c9) : 4r3c9 - - - - - - -                  |                |                               |                |      5r7c2 -> -7r7c2          |                |     |                         |                 4r2c2 (*)                      |                      |                         |                       5r3c2 -> 5r2c2 -> 7r5c5 -> 7r6c2 -> -7r7c2                 14r23c7 -> 2r6c7 -> 2r5c3 - - - - - - - - - - - -                 |                                                 |P(9r3c9) : 9r3c9                                                  |                |                                                 |                |                          5r7c2 -> -7r7c2        |                |                         |                       |                 9r2c3 -> 56r3c36 -> 4r3c2 (*)                    |                                          |                       |                                          5r2c2 -> 6r2c5 -> 7r6c5 -> 7r5c2 -> -7r7c2`
Last edited by Mauriès Robert on Tue Dec 17, 2019 8:48 pm, edited 1 time in total.
Mauriès Robert

Posts: 460
Joined: 07 November 2019
Location: France

### Re: Almost-binary puzzle

::Off Topic::
Hi qiuyanzhe, my apologies for posts out of your subject. Thanks
========================================================

Hi SpAce,
SpAce wrote:Many thanks for that diagram! Very interesting. Hodoku can't find such nets, probably due to the multi-kraken nature, so examples of logic like that are hard to come by. It is, however, perfectly understandable in your neat notation. Now I'm just wondering how best to search for such beasts manually. Any tips?

Thanks. I rarely try to find a complex move like this and in fact, I don't know how to explain how I had found that move, even by Vietnamese. It seems more difficult than solving puzzles
I don’t use Hodoku because of I have solve puzzles before Hoduku complete , I use Simple Sudoku (by Angus Johnson) to solve, SudoCue (by Ruud) to see stronglinks (bilocations) and of course SE to check rating. When I solve puzzles, at first I try to find as many stronglinks as I can after that I link them and see how far they go.
For this one – except many bivalue cells & bilocations, I find out some stronglinks that seems useful like: AUR(38)r56c29, AUR(48)r69c78, DP(14789)r2c89/r3c9, DP(4569)r2c235… but nothing has progressed until I find candidates (479)r3c9 (or maybe my lucky ).
See below grids for replacing r3c9=4 and r3c9=9. The rest, is how to present it readable. There is many way to present this move based on those grids. Then my lucky again, look at grids and see that R3C9, (5)C2, (7)R56 are core to present the move, so I intend to present it as diagram with triple krakens - R2C7 is extra situations.
Conclusion - of course for me only, hard WORKS & a little LUCKY !

Hidden Text: Show
Code: Select all
` *--------------------------------------------------* | 1    2    3    | 78   9    4    | 78   5    6    | | 7    456  569  | 18   56   2    | 149  3    489  | | 8    456  569  | 17   3    56   | 149  2    479  | |----------------+----------------+----------------| | 9    1    4    | 3    2    8    | 6    7    5    | | 6    378  278  | 4    57   15   | 29   18   389  | | 5    378  278  | 9    67   16   | 24   148  348  | |----------------+----------------+----------------| | 2    578  578  | 6    4    3    | 78   9    1    | | 4    9    1    | 5    8    7    | 3    6    2    | | 3    678  678  | 2    1    9    | 5    48   478  | *--------------------------------------------------*Replace r3c9=4: (7)r6c2=r6c5-(7=5)r5c5-r5c6=r3c6-r3c2=r7c2 => r7c2<>7  *-----------------------------------------* | 1   2   3   | 8   9   4   | 7   5   6   | | 7   4   56  | 1   56  2   | 9   3   8   | | 8   56  9   | 7   3   56  | 1   2   4   | |-------------+-------------+-------------| | 9   1   4   | 3   2   8   | 6   7   5   | | 6   3   78  | 4   57  15  | 2   18  9   | | 5   78  2   | 9   67  16  | 4   18  3   | |-------------+-------------+-------------| | 2   57  57  | 6   4   3   | 8   9   1   | | 4   9   1   | 5   8   7   | 3   6   2   | | 3   68  68  | 2   1   9   | 5   4   7   | *-----------------------------------------*Replace r3c9=9: (7)r5c2=(7-5)r5c5=r2c5-r2c2=r7c2 => r7c2<>7 *-----------------------------------------* | 1   2   3   | 8   9   4   | 7   5   6   | | 7   56  9   | 1   56  2   | 4   3   8   | | 8   4   56  | 7   3   56  | 1   2   9   | |-------------+-------------+-------------| | 9   1   4   | 3   2   8   | 6   7   5   | | 6   78  2   | 4   57  15  | 9   18  3   | | 5   3   78  | 9   67  16  | 2   18  4   | |-------------+-------------+-------------| | 2   57  57  | 6   4   3   | 8   9   1   | | 4   9   1   | 5   8   7   | 3   6   2   | | 3   68  68  | 2   1   9   | 5   4   7   | *-----------------------------------------*`

Note: in above grids you could also eliminate r7c2<>5

Hope above can a little clear for you.

SpAce wrote:I don't know if you're familiar with the concept, but if you are, would you agree that I captured your logic? I'm obviously using a slightly different approach from SteveK's by splitting the cases (4r3c9 and 9r3c9) vertically. Not only does it save horizontal space, but I think it's much more understandable with the two sub-matrices clearly separated.

I'm not familiar with Matrix, it's just one of the ways to present how to solve puzzles even that is a favorite of my Sudoku Mentor - Steve K .

totuan
totuan

Posts: 52
Joined: 25 May 2010
Location: vietnam

### Re: Almost-binary puzzle

Thanks a lot, again, totuan! I think I understand your process a bit better now, and I really appreciate it! It's not as mysterious if you break it into sub-problems and sub-grids like that. I'll have to try those ideas myself.

SpAce

Posts: 2674
Joined: 22 May 2017

### Re: Almost-binary puzzle

Hi Robert,

Mauriès Robert wrote:Here, below, in the TDP way, is a diagram equivalent to that of Totuan.

Only equivalent in its results. Note that it contains about half of the same information, even though it takes at least as much space. totuan's diagrams are easy to follow (even without seeing the grid) for the same reason why AICs are easy to follow (for those who understand the syntax), because they give detailed reasons for each implication.

Basic implication chains/nets do not because they only list the "placements". They require the reader to look at the grid at the same time and figure out why things happen as written. Such quantum jumps are much slower to read, even if there's enough information to avoid ambiguity. Nevertheless, your diagrams are still a big improvement to not having any at all.

I can see how your process has similarities to totuan's. Some purists might not be thrilled about the nested bifurcations, though. I think it's ok if the difficulty level warrants it and it's used to produce verities instead of contradictions. I'm mainly concerned about how best to use it, as such parallel OR-branches get hard to track in a single grid. Working with sub-grids, as presented by totuan, might be one relatively doable way.

Who is behind these diagrams?

I don't know who invented the concept (possibly totuan himself?), but at least totuan's diagrams are legendary in their clarity, unambiguity, and compact layout. Few if any can write them as well.

SpAce

Posts: 2674
Joined: 22 May 2017

### Re: Almost-binary puzzle

Who is behind these diagrams?

I don't know who invented the concept (possibly totuan himself?), but at least totuan's diagrams are legendary in their clarity, unambiguity, and compact layout. Few if any can write them as well.

the defunct programing forms, and the defunct sudoku.uk.org chat forum used them frequently - used by multiple old timers to represent SIS easiest.
it is a graphing method to map out nodes visited by a computer program. - doesn't really have a sudoku "inventor" so to speak as it was used in that field long before Sudoku.
sk did use them frequently on his blogs which totuan said was his mentor.
Some do, some teach, the rest look it up.

StrmCkr

Posts: 1205
Joined: 05 September 2006

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