## Hidden Numbers on Row/Column/Block

Advanced methods and approaches for solving Sudoku puzzles

### Hidden Numbers on Row/Column/Block

Hi all,
When study some hardest puzzles I found a way to solve them quite fast even rating SE 10.0 or higher. I do not know this way has ready yet on this Forum or other Site. The meaning of this way are looking for Hidden Pair-Triple –Quad… on Row/Column/Block (R/C/B).
Conditions :
1- Row/Column/Block had 3 or 4 given numbers.
2- Row/Column/Bock have to at least a candidate that this candidate is Strong Link on this R/C/B
3- Row/Column/Block have to at least a cell that this cell is only two candidates.

Example : A B C xy xyztsv xyztsv xytsv xytsv xytsv
- ABC : given numbers
- xyztsv : candidates

At present, I suggest some form based on this way:
FORM 1 : A B C xy xyzt xzs ytv tsv ysv => A B C xy xyz yz tv tsv sv

FORM 2 : A B C zy xyztsv xytsv xytsv xytsv xytsv => A B C zy zy xtsv xtsv xtsv xtsv

FORM 3 : A B C xy yzt xzsv xysv ytsv tsv => A B C xy yzt xz yt sv sv

……………………………………

I’m not enough smart, patient, time… to suggest more in this time.

EXAMPLE :

Code: Select all
`Original puzzle : Arto's Etana  - SE 10.5 *-----------* |1..|..7|.9.| |.3.|.2.|..8| |..9|6..|5..| |---+---+---| |..5|3..|9..| |.1.|.8.|..2| |6..|..4|...| |---+---+---| |3..|...|.1.| |.4.|...|..7| |..7|...|3..| *-----------* After basic eliminations : *-----------------------------------------------------------------------------* | 1       2568    2468    | 458     345     7       | 246     9       346     | | 457     3       46      | 1459    2       159     | 1467    467     8       | | 2478    278     9       | 6       134     138     | 5       2347    134     | |-------------------------+-------------------------+-------------------------| | 2478    278     5       | 3       167     126     | 9       4678    146     | | 479     1       34*     | 579     8       569     | 467     34567* 2        | | 6       2789    238     | 12579   1579    4       | 178     3578    135     | |-------------------------+-------------------------+-------------------------| | 3       25689   268     | 245789  45679   25689   | 2468    1       4569    | | 2589    4       1       | 2589    3569    235689  | 268     2568    7       | | 2589    25689   7       | 124589  14569   125689  | 3       24568   4569    | *-----------------------------------------------------------------------------*Row 5 : strong link 3’s at r5c3 & r5c8, based on Form 2 => pair 34 at r5c3 and r5c8 *-----------------------------------------------------------------------------* | 1       2568    2468    | 458     345     7       | 246     9       346     | | 457     3       46      | 1459    2       159     | 1467*   467     8       | | 2478    278     9       | 6       134     138     | 5       2347    134     | |-------------------------+-------------------------+-------------------------| | 2478    278     5       | 3       167     126     | 9       4678    146     | | 79      1       34      | 579     8       569     | 67*     34      2       | | 6       2789    238     | 1279    179     4       | 178*    3578    135     | |-------------------------+-------------------------+-------------------------| | 3       25689   268     | 245789  45679   25689   | 2468    1       4569    | | 2589    4       1       | 2589    3569    235689  | 268     2568    7       | | 2589    25689   7       | 124589  14569   125689  | 3       24568   4569    | *-----------------------------------------------------------------------------*Column 7 : strong link 1’s at r2c7&r6c7, based on Form 1 => triple 167 at r2c7, r5c7,r6c7   *-----------------------------------------------------------------------------* | 1       2568*   2468    | 458     345     7       | 24      9       346     | | 457*    3       46*     | 1459    2       159     | 167     467     8       | | 2478    278     9       | 6       134     138     | 5       2347    134     | |-------------------------+-------------------------+-------------------------| | 2478    278     5       | 3       167     126     | 9       4678    146     | | 79      1       34      | 579     8       569     | 67      34      2       | | 6       2789    238     | 1279    179     4       | 17      3578    135     | |-------------------------+-------------------------+-------------------------| | 3       25689   268     | 245789  45679   25689   | 248     1       4569    | | 2589    4       1       | 2589    3569    235689  | 28      256     7       | | 2589    25689   7       | 124589  14569   125689  | 3       2456    4569    | *-----------------------------------------------------------------------------*Now rating still SE 9.1.Block 1 : strong link 5’s at r1c2&r2c1, based on Form 3 => quad 4567 at r1c2, r2c1, r3c1, r2c3   *-----------------------------------------------------------------------------* | 1       56      28      | 458     345     7       | 24      9       346     | | 457     3       46      | 1459    2       159     | 167     467     8       | | 47      28      9       | 6       134     138     | 5       2347    134     | |-------------------------+-------------------------+-------------------------| | 248     278     5       | 3       167     126     | 9       4678    146     | | 9       1       34      | 57      8       56      | 67      34      2       | | 6       278     238     | 1279    179     4       | 17      3578    135     | |-------------------------+-------------------------+-------------------------| | 3       569     268     | 24578   4567    2568    | 248     1       459     | | 258     4       1       | 2589    3569    235689  | 28      256     7       | | 258     569     7       | 12458   1456    12568   | 3       2456    4569    | *-----------------------------------------------------------------------------*then  rating SE 8.4`

After all above I have questions :
1- This way is logic or as T&E?
2- If this way is logic then how to demonstrate?
3- Some more Form?

Thanks to all
TTT

Code: Select all
ttt

Posts: 185
Joined: 20 October 2006
Location: vietnam

removed
Last edited by StrmCkr on Sat Dec 13, 2014 6:36 am, edited 1 time in total.
Some do, some teach, the rest look it up.

StrmCkr

Posts: 858
Joined: 05 September 2006

ttt,

as i see it, this is another method you should only apply, if you know the solution

It is very clear, that you cannot make these eliminations based only on the candidates of one unit, as you suggest it with your FORM's. It would not be hard to find counter-examples, but your FORM's are too weird for me and i cannot see the relationship between them and your samples. Maybe you could add a mapping between the numbers in the samples and the characters in the FORM's.
ravel

Posts: 998
Joined: 21 February 2006

Hi RAVEL,

I did not know solution before apply my form to solve puzzle.
The meaning of my way based on a cell with only two candidates and a candidate that is strong link on Row/Column/Block (note that this candidate do not any other strong link on other Row/Column/Block) then I considerate 3 cells that contains 3 those candidates. As my questions on first post I’m not sure this way logic or not BUT if you apply my form to solve puzzle it is correct…

Example :
Code: Select all
`Original puzzle (from sudoku.com.au – tough  Dec. 20-2006 - Edit) : rating SE 9.0*-----------* |.4.|.2.|...| |...|..7|.8.| |.57|...|6..| |---+---+---| |.14|..6|..8| |...|.5.|...| |8..|1..|39.| |---+---+---| |..3|...|47.| |.2.|4..|...| |...|.9.|.1.| *-----------* after basic elimitations *-----------------------------------------------------------------------------* | 1369    4       8       | 3569    2       1359    | 1579    35      13579   | | 12369   369     1269*   | 3569    1346    7       | 1259    8       123459  | | 1239    5       7       | 389     1348    13489   | 6       234     12349   | |-------------------------+-------------------------+-------------------------| | 23579   1       4       | 2379    37      6       | 257     25      8       | | 23679   3679    269     | 23789   5       23489   | 127     246     12467   | | 8       67      256     | 1       47      24      | 3       9       24567   | |-------------------------+-------------------------+-------------------------| | 1569    689     3       | 2568    168     1258    | 4       7       2569    | | 15679   2       1569*   | 4       13678   1358    | 589     356     3569    | | 4       678     56*     | 235678  9       2358    | 258     1       2356    | *-----------------------------------------------------------------------------*  Column 3: only strong link 1’s at r2c3&r8c3 and r9c3=56, based on Form 1 => triple 156 at r289c3*-----------------------------------------------------------------------------* | 1369    4       8       | 3569    2       1359    | 1579    35      13579   | | 12369   369     16      | 3569    1346    7       | 1259    8       123459  | | 1239    5       7       | 389     1348    13489   | 6       234     12349   | |-------------------------+-------------------------+-------------------------| | 23579   1       4       | 2379    37      6       | 257     25      8       | | 23679   3679    9       | 23789   5       23489   | 127     246     12467   | | 8       67      2       | 1       47      24      | 3       9       24567   | |-------------------------+-------------------------+-------------------------| | 1569    689     3       | 2568    168     1258    | 4       7       2569    | | 15679   2       156     | 4       13678   1358    | 589     356     3569    | | 4       678     56      | 235678  9       2358    | 258     1       2356    | *-----------------------------------------------------------------------------*now rating SE 4.4`

Wow, my lucky…?
Last edited by ttt on Sat Mar 17, 2007 4:40 am, edited 1 time in total.
ttt

Posts: 185
Joined: 20 October 2006
Location: vietnam

In the first grid in block 4 there is the only strong link for 5 (r4c1, r6c3), 67 in r6c2 => triple 567 in r4c1, r6c3, r6c2. Bad luck.

btw, in your first sample above there are 4 strong links for 3. Any new rules now ?
ravel

Posts: 998
Joined: 21 February 2006

Hi RAVEL,
Block 4 : strong link 5's at (r4c1,r6c3) - (r6c3,r6c9) strong link 5's : Row 6, impossible to apply my form 1&3

not enough smart for more new rules now...
ttt

Posts: 185
Joined: 20 October 2006
Location: vietnam

Other example for applying my way - Form 2 :
Code: Select all
`Original puzzle : dml12  - SE 10.7*-----------* |..3|9..|...| |.4.|.7.|..1| |6..|..2|...| |---+---+---| |8..|...|..2| |.7.|.5.|.3.| |..9|...|4..| |---+---+---| |2..|..1|..8| |...|.4.|.5.| |...|6..|9..| *-----------*After basic elimination :   *--------------------------------------------------------------------* | 157    1258   3      | 9      168    4568   | 5678   24678  4567   | | 59*    4      258    | 358    7      3568   | 23568  2689   1      | | 6      1589*  1578   | 13458  138    2      | 3578   4789   34579  | |----------------------+----------------------+----------------------| | 8      1356   1456   | 1347   1369*  34679  | 1567   1679*  2      | | 14     7      1246   | 1248   5      4689   | 168    3      69*    | | 135    12356  9      | 12378  12368  3678   | 4      1678   567    | |----------------------+----------------------+----------------------| | 2      3569*  4567   | 357    39*    1      | 367    467    8      | | 1379   13689  1678   | 2378   4      3789   | 12     5      367    | | 13457  1358   14578  | 6      238    3578   | 9      12     347    | *--------------------------------------------------------------------*Block 1: strong link 9’s at (r2c1,r3c2) and r2c1=59, based on Form 2  => pair 59 at (r2c1,r3c2)Block 6: strong link 9’s at (r4c8,r5c9) and r5c9=69, based on Form 2  => pair 69 at (r4c8,r5c9) Row 7:   strong link 9’s at (r7c2,r7c5) and r7c5=39, based on Form 2  => pair 39 at (r7c2,r7c5)Col 5:   strong link 9’s at (r4c5,r7c5) and r7c5=39, based on Form 2  => pair 39 at (r4c2,r7c5) *--------------------------------------------------------------------* | 17     128    3      | 9      168    4568   | 5678   24678  4567   | | 59     4      28     | 358    7      3568   | 23568  2689   1      | | 6      59     178    | 13458  18     2      | 3578   4789   4579   | |----------------------+----------------------+----------------------| | 8      1356   1456   | 1347   39     34679  | 157    69     2      | | 14     7      1246   | 1248   5      4689   | 18     3      69     | | 135    12356  9      | 12378  1268   3678   | 4      178    57     | |----------------------+----------------------+----------------------| | 2      39     4567   | 57     39     1      | 67     467    8      | | 1379   13689  1678   | 2378   4      3789   | 12     5      367    | | 13457  1358   14578  | 6      28     3578   | 9      12     347    | *--------------------------------------------------------------------*now  rating SE 9.1`

My way with existing form gave up . Block 2 : strong link 4’s at (r1c6,r3c4) and r3c5=18 but (r3c5,r1c5) had already reduce on Column 5 then impossible to apply my form 1&3.
ttt

Posts: 185
Joined: 20 October 2006
Location: vietnam

ttt wrote:Block 4 : strong link 5's at (r4c1,r6c3) - (r6c3,r6c9) strong link 5's : Row 6, impossible to apply my form 1&3
You are right. Have you also noticed the strong link for 1 in row 5 ? So its impossible to apply your form there too ?
ttt wrote:Block 2 : strong link 4’s at (r1c6,r3c4) and r3c5=18 but (r3c5,r1c5) had already reduce on Column 5 then impossible to apply my form 1&3.
Aha, yet another rule.

I still dont know exactly, what your rules are or are not. You should take the time to formulate them in a clear way. Otherwise i will not waste more time with them.
ravel

Posts: 998
Joined: 21 February 2006

Hi RAVEL,

Thanks a lot. I will take the time (maybe long... ) to furmulate them in a clear way.
BTW, row 5 had not any cell with only 2 candidates.
ttt

Posts: 185
Joined: 20 October 2006
Location: vietnam

Hi RAVEL,

Sorry, But I would like to know : Why are you retied...!
ttt

Posts: 185
Joined: 20 October 2006
Location: vietnam