Hi experts,
I have got an idea about how to utilize only 5184 templates of 8 rows only (instead of 46656 templates of 9 rows) for all possible combination of each digit of a puzzle.
Just share the idea. Please do not hesitate to ask if explanation is needed.
// Global constant variable declaration with initializations
int P[5184][8];
int T[9][8] = { // Pointers to POM column for each puzzle column cell position containing digit
{ 1, 2, 3, 4, 5, 6, 7, 8}, { 0, 2, 3, 4, 5, 6, 7, 8}, { 0, 1, 3, 4, 5, 6, 7, 8},
{ 4, 5, 0, 1, 2, 6, 7, 8}, { 5, 3, 0, 1, 2, 6, 7, 8}, { 3, 4, 0, 1, 2, 6, 7, 8},
{ 7, 8, 0, 1, 2, 3, 4, 5}, { 6, 8, 0, 1, 2, 3, 4, 5}, { 6, 7, 0, 1, 2, 3, 4, 5}};
Note: Next, I am thinking about how to skip (jump) templates for remaining 8 rows.
int J[9] = {864, 288, 48, 12, 6, 2, 1, 0};
R. Jamil
Pattern Overlay Method
69 posts
• Page 3 of 5 • 1, 2, 3, 4, 5
Re: Pattern Overlay Method
by rjamil » Sun Oct 20, 2024 4:54 am
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Re: Pattern Overlay Method
by P.O. » Sun Oct 20, 2024 7:58 am
Hi R. Jamil, is it possible for you to use an example to detail the application of your ideas?
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Re: Pattern Overlay Method
by rjamil » Sun Oct 20, 2024 10:10 am
Hi P.O.,
Let me explain in detail shortly as I am now trying to code the same in highly optimized way. Also source code will be shared once finalized. Don't know how long it will take time.
Added: I have updated RJSudoku.c and RJSukaku.c solver in my GitHub. These programs included the unoptimized versions of POM.
Now I am working to implement my proposed optimization by removing the swap routine and skipping the templates as per described in my above post.
R. Jamil
P.O. wrote:Hi R. Jamil, is it possible for you to use an example to detail the application of your ideas?
Let me explain in detail shortly as I am now trying to code the same in highly optimized way. Also source code will be shared once finalized. Don't know how long it will take time.
Added: I have updated RJSudoku.c and RJSukaku.c solver in my GitHub. These programs included the unoptimized versions of POM.
Now I am working to implement my proposed optimization by removing the swap routine and skipping the templates as per described in my above post.
R. Jamil
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- Location: Karachi, Pakistan
Re: Pattern Overlay Method
by yzfwsf » Sun Oct 20, 2024 11:20 pm
Hi P.O.
I think if you include hidden single, you don't need to combine templates to exclude some invalid templates.
I think if you include hidden single, you don't need to combine templates to exclude some invalid templates.
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Re: Pattern Overlay Method
by P.O. » Mon Oct 21, 2024 3:24 am
Hi yzfwsf, my Singles procedure includes naked and hidden single.
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Re: Pattern Overlay Method
by yzfwsf » Mon Oct 21, 2024 3:44 am
What I mean is that the POM process should add the function of Hidden Single, so as to reduce unnecessary combinations.
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Re: Pattern Overlay Method
by P.O. » Mon Oct 21, 2024 3:57 am
my pom procedure uses Singles and therefore both naked and hidden single
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Re: Pattern Overlay Method
by rjamil » Tue Oct 22, 2024 1:35 pm
Hi experts,
I have an idea to speed up the searching procedure of POM, without swapping and complexity, by adding a reference table of two dimensional array T[9, 60] containing 8 remaining disjoint subset of particular digit for each first row's cell; and, with template skipping as proposed earlier.
Here I am sharing disjoint cells reference table:
Where as:
0-6 position represent 2nd row disjoint cells;
6-11 => 3rd;
12-19 => 4th;
20-27 => 5th;
28-35 => 6th;
36-43 => 7th;
44-51 => 8th; and
52-59 => 9th.
I will then temper the Myth Jellies POM Template stored in two dimensional array of 46656 X 9 elements, by giving credit to him, as follows:
I'll take only the first 5184 rows X 8 columns, omitting rest of the 41,472 rows X first column.
Now, carefully change the first column values from 12-17 to 0-5;
second => from 21-26 to 6-11;
third => from 28-35 to 12-19;
fourth => from 37-44 to 20-27;
fifth => from 46-53 to 28-35;
sixth => from 55-62 to 36-43;
seventh => from 64-71 to 44-51; and
eight => from 73-80 to 52-59.
In this way, I will be able to point each templates to its corresponding reference table, which is pre-ordered reference to the original Sudoku grid.
This will definitely made an ultra fast POM searching routine.
Hope my above proposed logic is understandable for everyone.
R. Jamil
I have an idea to speed up the searching procedure of POM, without swapping and complexity, by adding a reference table of two dimensional array T[9, 60] containing 8 remaining disjoint subset of particular digit for each first row's cell; and, with template skipping as proposed earlier.
Here I am sharing disjoint cells reference table:
Hidden Text: Show
Where as:
0-6 position represent 2nd row disjoint cells;
6-11 => 3rd;
12-19 => 4th;
20-27 => 5th;
28-35 => 6th;
36-43 => 7th;
44-51 => 8th; and
52-59 => 9th.
I will then temper the Myth Jellies POM Template stored in two dimensional array of 46656 X 9 elements, by giving credit to him, as follows:
I'll take only the first 5184 rows X 8 columns, omitting rest of the 41,472 rows X first column.
Now, carefully change the first column values from 12-17 to 0-5;
second => from 21-26 to 6-11;
third => from 28-35 to 12-19;
fourth => from 37-44 to 20-27;
fifth => from 46-53 to 28-35;
sixth => from 55-62 to 36-43;
seventh => from 64-71 to 44-51; and
eight => from 73-80 to 52-59.
In this way, I will be able to point each templates to its corresponding reference table, which is pre-ordered reference to the original Sudoku grid.
This will definitely made an ultra fast POM searching routine.
Hope my above proposed logic is understandable for everyone.
R. Jamil
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- Location: Karachi, Pakistan
Re: Pattern Overlay Method
by P.O. » Tue Oct 22, 2024 5:03 pm
Hi R Jamil, an example with a puzzle would be welcome to understand what you are doing
- P.O.
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- Joined: 07 June 2021
Re: Pattern Overlay Method
by rjamil » Thu Oct 24, 2024 1:40 am
Hi P.O.,
If you are familiar with my tempered POM, disjoint cells reference table and POM skips/jumps then I am going to show you how to search POM eliminations and placements as follows:
I have stored Sudoku puzzle in two different arrays, i.e., s[81] contain clues + solved; and g[81] contain pencilmarks.
1) for x = 1; x < 10; ++x // for each digit
2) k[81] = {0}; // assign array holding digit count, initializing with 0's
3) for y = 0; y < 9; ++y // for each cell in first row
4) if s[y] or g[y] not contain digit x then goto 3 // if digit not found in cell
5) for z = 0; z < 5184; z += 864 // loop for each POM template
6) for a = 0; a < 8; ++a // loop for each POM cell
7) if s[t[p[z][a]] or g[t[p[z][a]] not contain digit x then goto 5
8) next a
9) if a > 7 then increment each cell in k array as digit count
10) next z
...
Hope my above logic is simple to understand as I am yet to start coding/programming.
R. Jamil
Added as on 20241026: Wish to inform that, I have implemented the template skipping/stepping in POM routine and updated my GitHub site. Now, working on removal of the swap routine, without loosing any scenario. My POM routine will then become robust and exhaustive.
Slightly change the values of T[8] = {863,287,47,11, 5, 1, 0, 0}
Added as on 20241104: wish to inform that, after very hard effort spent on several hours, I finally managed to remove the swap routine from the pattern overlay method.
For this only 3 x 5184 x 8 templates have to be used instead of 5184 x 8 or 46656 x 9. While 9 x 60 reference array and stepping have to be used۔
For rest of the details after cleaning and completing the code, will share the final source code with explanation here shortly.
P.O. wrote:Hi R Jamil, an example with a puzzle would be welcome to understand what you are doing
If you are familiar with my tempered POM, disjoint cells reference table and POM skips/jumps then I am going to show you how to search POM eliminations and placements as follows:
I have stored Sudoku puzzle in two different arrays, i.e., s[81] contain clues + solved; and g[81] contain pencilmarks.
1) for x = 1; x < 10; ++x // for each digit
2) k[81] = {0}; // assign array holding digit count, initializing with 0's
3) for y = 0; y < 9; ++y // for each cell in first row
4) if s[y] or g[y] not contain digit x then goto 3 // if digit not found in cell
5) for z = 0; z < 5184; z += 864 // loop for each POM template
6) for a = 0; a < 8; ++a // loop for each POM cell
7) if s[t[p[z][a]] or g[t[p[z][a]] not contain digit x then goto 5
8) next a
9) if a > 7 then increment each cell in k array as digit count
10) next z
...
Hope my above logic is simple to understand as I am yet to start coding/programming.
R. Jamil
Added as on 20241026: Wish to inform that, I have implemented the template skipping/stepping in POM routine and updated my GitHub site. Now, working on removal of the swap routine, without loosing any scenario. My POM routine will then become robust and exhaustive.
Slightly change the values of T[8] = {863,287,47,11, 5, 1, 0, 0}
Added as on 20241104: wish to inform that, after very hard effort spent on several hours, I finally managed to remove the swap routine from the pattern overlay method.
For this only 3 x 5184 x 8 templates have to be used instead of 5184 x 8 or 46656 x 9. While 9 x 60 reference array and stepping have to be used۔
For rest of the details after cleaning and completing the code, will share the final source code with explanation here shortly.
- rjamil
- Posts: 785
- Joined: 15 October 2014
- Location: Karachi, Pakistan
Re: Pattern Overlay Method
by P.O. » Thu Nov 14, 2024 6:45 am
hi R.Jamil, thanks for sharing your work
what you show corresponds for me to the initialization phase before any combination of templates is made and here are the differences that i see in our ways of doing things
- i only use Singles to update the resolution state, especially as Myth Jellies pointed out, i quote:
(POM) "finds every single-digit reduction possible at that point in the puzzle. All locked candidates, x-wings, swordfish, jellyfish, finned fish, simple coloring, strong links, multi-coloring, grouped multi-coloring, x-cycles, grouped x-cycles, and franken-fish reductions for any converted digits are found"
all these eliminations are found by simply examining the templates.
- i first check if there are candidates that can be set as is the case here for r3c5=6 and then i immediately update the resolution state with Singles, which here has the effect of putting in addition to r3c5=6 22 other placements.
- i recompute all the templates and here their examination makes me find 21 eliminations accompanied by 2 placements.
- i do another update of the templates and i find nothing more
the next phase is to start the combinations from the following situation:
what you show corresponds for me to the initialization phase before any combination of templates is made and here are the differences that i see in our ways of doing things
- i only use Singles to update the resolution state, especially as Myth Jellies pointed out, i quote:
(POM) "finds every single-digit reduction possible at that point in the puzzle. All locked candidates, x-wings, swordfish, jellyfish, finned fish, simple coloring, strong links, multi-coloring, grouped multi-coloring, x-cycles, grouped x-cycles, and franken-fish reductions for any converted digits are found"
all these eliminations are found by simply examining the templates.
- i first check if there are candidates that can be set as is the case here for r3c5=6 and then i immediately update the resolution state with Singles, which here has the effect of putting in addition to r3c5=6 22 other placements.
- i recompute all the templates and here their examination makes me find 21 eliminations accompanied by 2 placements.
- i do another update of the templates and i find nothing more
the next phase is to start the combinations from the following situation:
- Code: Select all
12357 12347 123457 2345 1245 1245 8 9 6
13568 1346 13458 3456 9 1458 2 145 7
9 12346 123458 7 124568 12458 134 145 1345
12 1249 1249 24569 3 124589 1469 7 124589
1237 5 6 249 12478 124789 1349 1248 123489
1237 8 123479 24569 124567 124579 13469 12456 123459
2378 2379 23789 1 247 6 5 248 2489
4 12679 125789 259 257 2579 1679 3 1289
12567 12679 12579 8 2457 3 14679 1246 1249
275 candidates.
#VT: (686 874 24 282 82 5 29 6 36)
Cells: nil nil nil nil nil (23) nil nil nil
SetVC: ( n6r3c5 n8r5c5 n8r7c8 n8r4c9 n8r8c3 n8r2c1
n6r2c2 n6r9c1 n8r3c6 n5r9c3 n5r1c1 n6r6c8
n6r8c7 n7r9c7 n5r6c9 n6r4c4 n5r8c5 n5r4c6
n5r3c8 n5r2c4 n3r1c4 n3r2c3 n3r7c2 )
#VT: (17 28 3 21 1 1 3 1 10)
Cells: nil nil nil nil nil nil nil nil nil
Candidates:(2 20 29 30 48) (2 3 37 40 42 46 48) nil (5 42 50 51) nil nil (48 55) nil (45 65 72)
EraseCC: ( n2r7c1 n1r4c1 )
#VT: (10 14 3 21 1 1 3 1 10)
Cells: nil nil nil nil nil nil nil nil nil
Candidates:nil nil nil nil nil nil nil nil nil
5 47 147 3 12 124 8 9 6
8 6 3 5 9 14 2 14 7
9 24 124 7 6 8 134 5 134
1 249 249 6 3 5 49 7 8
37 5 6 49 8 179 1349 124 1234
37 8 49 249 127 1279 1349 6 5
2 3 79 1 47 6 5 8 49
4 17 8 29 5 279 6 3 12
6 19 5 8 24 3 7 124 1249
95 candidates.
- P.O.
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- Joined: 07 June 2021
Re: Pattern Overlay Method
by rjamil » Thu Nov 14, 2024 1:18 pm
Hi P.O.,
Many thanks for replying with your fruitful findings.
I coded my POM routine robust and exhaustive (It does not mean that someone else will not find a way faster than mine. However, I checked and confirmed that my routine is exhaustive (However expert opinion/criticism are always welcome.)
I never intended to code any technique for separate checking purpose. But, my understanding is that, to search POM after all basic moves exhausted, and, check all digit one by one in a single go.
Hope, my POM routine works as last resort but before guessing, just like Andrew Stuart's did in his online solver.
Basically, I programmed vanilla Sudoku solver for bulk puzzle solving with minimum guessing. I only understand pattern based logic and trying to code for speed and minimum to none duplicate searching criteria in mind.
However, my program is free to use personally, and easy to exclude/commented any technique if one need to do so.
R. Jamil
Many thanks for replying with your fruitful findings.
I coded my POM routine robust and exhaustive (It does not mean that someone else will not find a way faster than mine. However, I checked and confirmed that my routine is exhaustive (However expert opinion/criticism are always welcome.)
I never intended to code any technique for separate checking purpose. But, my understanding is that, to search POM after all basic moves exhausted, and, check all digit one by one in a single go.
Hope, my POM routine works as last resort but before guessing, just like Andrew Stuart's did in his online solver.
Basically, I programmed vanilla Sudoku solver for bulk puzzle solving with minimum guessing. I only understand pattern based logic and trying to code for speed and minimum to none duplicate searching criteria in mind.
However, my program is free to use personally, and easy to exclude/commented any technique if one need to do so.
R. Jamil
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- Location: Karachi, Pakistan
Re: Pattern Overlay Method
by rjamil » Thu Nov 14, 2024 8:14 pm
Hi again,
After commented all technics from RJSudoku.c. Only singleton, POM and guess remain, following results obtain:
R. Jamil
After commented all technics from RJSudoku.c. Only singleton, POM and guess remain, following results obtain:
- Code: Select all
....47...8......9.....3....2.....7.5.6.9...........3...13.........6...8.4.7......#17September24
+----------------------+------------------------+------------------------+
| 13569 2359 12569 | 1258 4 7 | 12568 12356 12368 |
| 8 23457 12456 | 125 1256 1256 | 12456 9 123467 |
| 15679 24579 124569 | 1258 3 125689 | 124568 124567 124678 |
+----------------------+------------------------+------------------------+
| 2 3489 1489 | 1348 168 13468 | 7 146 5 |
| 1357 6 1458 | 9 12578 123458 | 1248 124 1248 |
| 1579 45789 14589 | 124578 125678 124568 | 3 1246 124689 |
+----------------------+------------------------+------------------------+
| 569 1 3 | 24578 25789 24589 | 24569 24567 24679 |
| 59 259 259 | 6 12579 123459 | 12459 8 123479 |
| 4 2589 7 | 12358 12589 123589 | 12569 12356 12369 |
+----------------------+------------------------+------------------------+
1st) Hidden single: 9 @ r3c6 from values 125689 Box 2 wise
2nd) Hidden single: 9 @ r6c9 from values 124689 Box 6 wise
3rd) Hidden single: 6 @ r7c1 from values 569 Box 7 wise
4th) Hidden single: 8 @ r9c2 from values 2589 Box 7 wise
+--------------------+------------------------+------------------------+
| 1359 2359 12569 | 1258 4 7 | 12568 12356 12368 |
| 8 23457 12456 | 125 1256 1256 | 12456 9 123467 |
| 157 2457 12456 | 1258 3 9 | 124568 124567 124678 |
+--------------------+------------------------+------------------------+
| 2 349 1489 | 1348 168 13468 | 7 146 5 |
| 1357 6 1458 | 9 12578 123458 | 1248 124 1248 |
| 157 457 1458 | 124578 125678 124568 | 3 1246 9 |
+--------------------+------------------------+------------------------+
| 6 1 3 | 24578 25789 2458 | 2459 2457 247 |
| 59 259 259 | 6 12579 12345 | 12459 8 12347 |
| 4 8 7 | 1235 1259 1235 | 12569 12356 1236 |
+--------------------+------------------------+------------------------+
4) POM: Digit 2 in r1c234789 r2c2345679 r3c234789 r4c1 r5c56789 r6c4568 r7c456789 r8c235679 r9c456789
Digit 2 not in 576 Templates => -2 @ r8c5 r8c6 r8c7 r8c9
4) POM: Digit 3 in r1c1289 r2c29 r3c5 r4c246 r5c16 r6c7 r7c3 r8c69 r9c4689
Digit 3 not in 5 Templates => -3 @ r1c1 r4c2 r5c6
Digit 3 in all 5 Templates => 3 @ r5c1
4) POM: Digit 5 in r1c123478 r2c234567 r3c123478 r4c9 r5c356 r6c123456 r7c45678 r8c123567 r9c45678
Digit 5 not in 432 Templates => -5 @ r8c5 r8c6 r8c7
4) POM: Digit 6 in r1c3789 r2c35679 r3c3789 r4c568 r5c2 r6c568 r7c1 r8c4 r9c789
Digit 6 not in 16 Templates => -6 @ r1c8 r2c3 r2c7 r2c9 r3c8 r9c8
4) POM: Digit 7 in r1c6 r2c29 r3c1289 r4c7 r5c5 r6c1245 r7c4589 r8c59 r9c3
Digit 7 not in 1 Template => -7 @ r2c9 r3c1 r3c2 r3c9 r6c2 r6c4 r6c5 r7c5 r7c8 r7c9 r8c5
Digit 7 in all 1 Template => 7 @ r2c2 r3c8 r5c5 r6c1 r7c4 r8c9
4) POM: Digit 8 in r1c479 r2c1 r3c479 r4c3456 r5c3679 r6c3456 r7c56 r8c8 r9c2
Digit 8 not in 16 Templates => -8 @ r4c4 r5c3 r5c6 r6c4
4) POM: Digit 9 in r1c123 r2c8 r3c6 r4c23 r5c4 r6c9 r7c57 r8c12357 r9c57
Digit 9 not in 8 Templates => -9 @ r8c5 r8c7
+------------------+---------------------+---------------------+
| 159 2359 12569 | 1258 4 7 | 12568 1235 12368 |
| 8 7 1245 | 125 1256 1256 | 1245 9 1234 |
| 15 245 12456 | 1258 3 9 | 124568 7 12468 |
+------------------+---------------------+---------------------+
| 2 49 1489 | 134 168 13468 | 7 146 5 |
| 3 6 145 | 9 7 1245 | 1248 124 1248 |
| 7 45 1458 | 1245 12568 124568 | 3 1246 9 |
+------------------+---------------------+---------------------+
| 6 1 3 | 7 2589 2458 | 2459 245 24 |
| 59 259 259 | 6 1 134 | 14 8 7 |
| 4 8 7 | 1235 1259 1235 | 12569 1235 1236 |
+------------------+---------------------+---------------------+
stte
- Code: Select all
....46...1......8.....3....2.....6.5.5.8...........3...13.........5...7.4.6......#17August24
+-----------------------+------------------------+-------------------------+
| 35789 23789 25789 | 1279 4 6 | 12579 12359 12379 |
| 1 234679 24579 | 279 2579 2579 | 24579 8 234679 |
| 56789 246789 245789 | 1279 3 125789 | 124579 124569 124679 |
+-----------------------+------------------------+-------------------------+
| 2 34789 14789 | 13479 179 13479 | 6 149 5 |
| 3679 5 1479 | 8 12679 123479 | 12479 1249 12479 |
| 6789 46789 14789 | 124679 125679 124579 | 3 1249 124789 |
+-----------------------+------------------------+-------------------------+
| 5789 1 3 | 24679 26789 24789 | 24589 24569 24689 |
| 89 289 289 | 5 12689 123489 | 12489 7 1234689 |
| 4 2789 6 | 12379 12789 123789 | 12589 12359 12389 |
+-----------------------+------------------------+-------------------------+
1st) Hidden single: 8 @ r3c6 from values 125789 Box 2 wise
2nd) Hidden single: 8 @ r6c9 from values 124789 Box 6 wise
3rd) Hidden single: 5 @ r7c1 from values 5789 Box 7 wise
4th) Hidden single: 7 @ r9c2 from values 2789 Box 7 wise
+--------------------+------------------------+------------------------+
| 3789 2389 25789 | 1279 4 6 | 12579 12359 12379 |
| 1 23469 24579 | 279 2579 2579 | 24579 8 234679 |
| 679 2469 24579 | 1279 3 8 | 124579 124569 124679 |
+--------------------+------------------------+------------------------+
| 2 3489 14789 | 13479 179 13479 | 6 149 5 |
| 3679 5 1479 | 8 12679 123479 | 12479 1249 12479 |
| 679 469 1479 | 124679 125679 124579 | 3 1249 8 |
+--------------------+------------------------+------------------------+
| 5 1 3 | 24679 26789 2479 | 2489 2469 2469 |
| 89 289 289 | 5 12689 12349 | 12489 7 123469 |
| 4 7 6 | 1239 1289 1239 | 12589 12359 1239 |
+--------------------+------------------------+------------------------+
4) POM: Digit 1 in r1c4789 r2c1 r3c4789 r4c34568 r5c356789 r6c34568 r7c2 r8c5679 r9c456789
Digit 1 not in 144 Templates => -1 @ r4c4 r6c4 r9c4
4) POM: Digit 2 in r1c234789 r2c2345679 r3c234789 r4c1 r5c56789 r6c4568 r7c456789 r8c235679 r9c456789
Digit 2 not in 576 Templates => -2 @ r8c5 r8c6 r8c7 r8c9
4) POM: Digit 3 in r1c1289 r2c29 r3c5 r4c246 r5c16 r6c7 r7c3 r8c69 r9c4689
Digit 3 not in 5 Templates => -3 @ r1c1 r4c2 r5c6
Digit 3 in all 5 Templates => 3 @ r5c1
4) POM: Digit 5 in r1c378 r2c3567 r3c378 r4c9 r5c2 r6c56 r7c1 r8c4 r9c78
Digit 5 not in 8 Templates => -5 @ r2c3 r2c7
4) POM: Digit 6 in r1c6 r2c29 r3c1289 r4c7 r5c5 r6c1245 r7c4589 r8c59 r9c3
Digit 6 not in 1 Template => -6 @ r2c9 r3c1 r3c2 r3c9 r6c2 r6c4 r6c5 r7c5 r7c8 r7c9 r8c5
Digit 6 in all 1 Template => 6 @ r2c2 r3c8 r5c5 r6c1 r7c4 r8c9
4) POM: Digit 7 in r1c13479 r2c345679 r3c13479 r4c3456 r5c3679 r6c3456 r7c56 r8c8 r9c2
Digit 7 not in 48 Templates => -7 @ r1c3 r2c3 r3c3 r5c3 r5c6
4) POM: Digit 8 in r1c123 r2c8 r3c6 r4c23 r5c4 r6c9 r7c57 r8c12357 r9c57
Digit 8 not in 8 Templates => -8 @ r8c5 r8c7
4) POM: Digit 9 in r1c1234789 r2c345679 r3c123479 r4c234568 r5c36789 r6c234568 r7c56789 r8c123567 r9c456789
Digit 9 not in 1536 Templates => -9 @ r8c5 r8c6 r8c7
+------------------+---------------------+----------------------+
| 789 2389 2589 | 1279 4 6 | 12579 12359 12379 |
| 1 6 249 | 279 2579 2579 | 2479 8 23479 |
| 79 249 2459 | 1279 3 8 | 124579 6 12479 |
+------------------+---------------------+----------------------+
| 2 489 14789 | 3479 179 13479 | 6 149 5 |
| 3 5 149 | 8 6 1249 | 12479 1249 12479 |
| 6 49 1479 | 2479 12579 124579 | 3 1249 8 |
+------------------+---------------------+----------------------+
| 5 1 3 | 6 2789 2479 | 2489 249 249 |
| 89 289 289 | 5 1 134 | 14 7 6 |
| 4 7 6 | 239 1289 1239 | 12589 12359 1239 |
+------------------+---------------------+----------------------+
stte
R. Jamil
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- Posts: 785
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- Location: Karachi, Pakistan
Re: Pattern Overlay Method
by P.O. » Fri Nov 15, 2024 5:49 am
i find the same eliminations which correspond to those mentioned above in the quote from Myth Jellies but the real power of a template procedure as a solving technique begins with the combinations of templates which consists of testing the compatibility of templates for different values and gradually eliminating all those which do not fit into any of them.
Do you intend to develop your procedure in this way?
Do you intend to develop your procedure in this way?
- P.O.
- Posts: 1764
- Joined: 07 June 2021
69 posts
• Page 3 of 5 • 1, 2, 3, 4, 5
