The New Sudoku Players' Forum

by **ttt** » Fri Mar 02, 2007 7:56 am

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
- z : strong link

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

by **StrmCkr** » Fri Mar 02, 2007 8:24 am

removed

by **ravel** » Fri Mar 02, 2007 2:58 pm

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.

by **ttt** » Fri Mar 02, 2007 6:30 pm

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…?

by **ravel** » Fri Mar 02, 2007 7:02 pm

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 ?

by **ttt** » Sat Mar 03, 2007 3:57 am

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...

by **ttt** » Sat Mar 03, 2007 10:23 am

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.

by **ravel** » Sat Mar 03, 2007 12:37 pm

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.

by **ttt** » Sat Mar 03, 2007 3:00 pm

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.

by **ttt** » Sat Nov 10, 2007 4:56 pm

Hi RAVEL,

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

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