The New Sudoku Players' Forum

by **udosuk** » Wed Oct 25, 2006 5:17 am

Ruud wrote:A new record: 592 candidates, 1 solution...

Great achievement!

Getting closer and closer to the magical 600 mark...

Code: Select all: 757 365 777 773 640 654 713 777 777 766 777 362 320 340 760 762 740 776 767 777 377 777 773 536 737 757 517 577 777 777 537 677 777 327 206 533 767 775 757 737 777 777 627 677 737 777 735 777 377 775 736 737 776 735 775 771 773 573 573 777 573 773 551 734 775 354 777 365 777 777 777 575 775 331 777 277 675 777 763 257 777 757365777773640654713777777766777362320340760762740776767777377777773536737757517 577777777537677777327206533767775757737777777627677737777735777377775736737776735 775771773573573777573773551734775354777365777777777575775331777277675777763257777

Quite interesting is the "complementary pencilmarks":

Code: Select all: 5 168 . 7 356789 3589 457 . . 69 . 1679 146789 156789 6789 679 56789 9 6 . 1 . 7 249 4 5 245 2 . . 24 3 . 146 134569 247 6 8 5 4 . . 346 3 4 . 48 . 1 8 49 4 9 48 8 78 7 27 27 . 27 7 2578 489 8 1589 . 168 . . . 28 8 1478 . 13 38 . 67 135 .

by **Ruud** » Wed Oct 25, 2006 1:05 pm

udosuk wrote:Getting closer and closer to the magical 600 mark...

Very close indeed

598 candidates

Code: Select all: 12345689 23456789 12345689 1245678 1234567 1456789 1456789 12356789 123456789 1234589 12346789 12346789 123456789 12578 12356789 146789 1235789 1356789 12345789 12346789 12346789 123456789 1234567 1235789 13456789 18 136789 13456789 23456789 4679 12346789 123456789 123456789 2467 123456789 145679 1356789 236789 2346789 124568 123456789 123456789 12345679 123456789 134679 1234589 123456789 123456789 12458 123458 123589 12345679 123456789 12345679 125789 12356789 12356789 123456789 123456789 12356789 2345678 124578 123456789 123456789 2356789 23456789 12345679 2345679 123456789 34567 1234578 23456789 12356789 36789 12356789 1356789 12356789 12356789 123456789 123578 35678

1 solution

Code: Select all: 952731864413685927786942513149263785328574196567819342835496271274158639691327458

compact notation

Code: Select all: 776 677 776 373 771 177 177 767 777 736 757 757 777 323 767 157 727 576 737 757 757 777 771 727 577 102 547 577 677 055 757 777 777 251 777 175 567 647 657 372 777 777 775 777 555 736 777 777 332 732 726 775 777 775 327 767 767 777 777 767 673 333 777 777 667 677 775 675 777 471 733 677 767 447 767 567 767 767 777 723 463

complementary candidate grid

Code: Select all: 7 1 7 39 89 23 23 4 . 67 5 5 . 3469 4 235 46 24 6 5 5 . 89 46 2 2345679 245 2 1 12358 5 . . 13589 . 238 24 145 15 379 . . 8 . 258 67 . . 3679 679 467 8 . 8 346 4 4 . . 4 19 369 . . 14 1 8 18 . 1289 69 1 4 1245 4 24 4 4 . 469 1249

With the complementary grid, it is easier to spot the single 4 in row 9, followed by a single 4 in box 3.

by **gsf** » Wed Oct 25, 2006 1:07 pm

Ruud wrote:A new record: 592 candidates, 1 solution.

nice job Ruud

[ edit: multiple solution puzzle deleted -- still can't crack 500 -- sorry for any confusion ]

by **Pyrrhon** » Thu Oct 26, 2006 4:25 pm

Here is my purpose:

622 candidates, 1 solution, solvable with logic steps by humans

Code: Select all: 123456789 123456789 123456789 123456789 123456789 123456789 123456789 158 58 12345679 12345679 12345679 139 12345679 12345679 12345679 123456789 12345679 3457 123456789 123456789 123456789 123456789 123456789 123456789 123456789 123456789 3457 123456789 34 123456789 123456789 123456789 234 123456789 123456789 123456789 123456789 123456789 148 123456789 123456789 24 123456789 123456789 12345679 12345679 12345679 123456789 12345679 12345679 12345679 123456789 12345679 25 123456789 123456789 123456789 2457 123456789 26 123456789 123456789 123456789 123456789 123456789 123456789 167 123456789 123456789 168 123456789 123456789 15 123456789 123456789 123456789 123456789 123456789 123456789 123456789

Solution in tiny text:

829463715
475912683
361785942
784256391
956137428
132894576
598641237
243578169
617329854

by **Ruud** » Thu Oct 26, 2006 4:56 pm

[obsolete post deleted]

by **JPF** » Thu Oct 26, 2006 5:06 pm

An easy way to build a table with 593 candidates :

Take a 17 clues valid puzzle.
For each empty cell : 9 candidates
For each cell with a clue : 1 candidate equal to the clue.

We get (81-17) x 9 + 17 = 593 candidates.

Am I missing something ?

JPF

by **gsf** » Thu Oct 26, 2006 5:09 pm

Pyrrhon wrote:Here is my purpose:

629 candidates, 1 solution, solvable with logic steps by humans

this puzzle has 7,408,714 solutions

by **gsf** » Thu Oct 26, 2006 5:12 pm

JPF wrote:We get (81-17) x 9 + 17 = 593 candidates.
Am I missing something ?

N candidates, no cell with less than 2 candidates

by **JPF** » Thu Oct 26, 2006 5:18 pm

thanks gsf.
I missed that point.

JPF

by **Pyrrhon** » Thu Oct 26, 2006 5:26 pm

Thanx Ruud and gsf, there was a failure in transcribing of cell R9C2 and a consecutive fault in counting, both are corrected now in my original post.

Pyrrhon

by **daj95376** » Thu Oct 26, 2006 6:32 pm

Pyrrhon wrote:Thanx Ruud and gsf, there was a failure in transcribing of cell R9C2 and a consecutive fault in counting, both are corrected now in my original post.

Pyrrhon

Impressive PM Sudoku ... and such a simple solution. It's interesting where starting with one Hidden Single can lead.

by **gsf** » Thu Oct 26, 2006 7:03 pm

Pyrrhon wrote:Thanx Ruud and gsf, there was a failure in transcribing of cell R9C2 and a consecutive fault in counting, both are corrected now in my original post.

singles reduce the puzzle to this

Code: Select all: 8 279 29 | 4 6 3 | 79 1 5 46 4567 567 | 9 1 2 | 67 8 3 3 69 1 | 7 8 5 | 69 4 2 ---------------+---------------+--------------- 7 8 4 | 2 5 6 | 3 9 1 9 56 56 | 1 3 7 | 4 2 8 1 23 23 | 8 9 4 | 5 7 6 ---------------+---------------+--------------- 5 79 8 | 6 4 1 | 2 3 79 2 349 39 | 5 7 8 | 1 6 49 46 1 67 | 3 2 9 | 8 5 47

what's the next move?

by **Pyrrhon** » Thu Oct 26, 2006 7:22 pm

Hint in tiny text:
The next move could be a xy-wing or a xyz-wing. If made both, the rest are singles.

by **Ruud** » Thu Oct 26, 2006 9:53 pm

Great achievement, Pyrrhon!

Human intelligence boldly goes where no computer has gone before...

Just for the record books, a maximized version of your grid:

623 candidates, same solution, same level of difficulty.

Code: Select all: 123456789 123456789 123456789 123456789 123456789 123456789 123456789 158 58 12345679 12345679 12345679 1359 12345679 12345679 12345679 123456789 12345679 3457 123456789 123456789 123456789 123456789 123456789 123456789 123456789 123456789 3457 123456789 34 123456789 123456789 123456789 234 123456789 123456789 123456789 123456789 123456789 148 123456789 123456789 24 123456789 123456789 12345679 12345679 12345679 123456789 12345679 12345679 12345679 123456789 12345679 25 123456789 123456789 123456789 2457 123456789 26 123456789 123456789 123456789 123456789 123456789 123456789 167 123456789 123456789 168 123456789 123456789 15 123456789 123456789 123456789 123456789 123456789 123456789 123456789

Ruud

by **Pyrrhon** » Fri Oct 27, 2006 5:00 am

I have made only two attempts for pencilmark only sudoku. The second one had lead to 618 candidates. So for sure a computer can top it, if somebody implements my way. My way was like the following:

1) Take a 17 given sudoku that you can solve.
2) Set all empty cells to 123456789 and the cells with a given digit get this given digit as candidate
3) Attempt step by step to each cell with only one candidate to add any other digit (only one) in a way so that you can still solve the puzzle, if not possible let the single candidate in this cell
4) Attempt to the cells with only one candidate to make hidden singles in a row, line or block in way where you must not delete a candidate in any bivalued cell. If possible you can set this cell to 123456789 and you must delete this candidate in the other cells. (If such hidden single is not possible you can delete the second value in the bivalued cell with a hidden single itself.)
5) If you have now at least 2 candidates in all cells you can look whether it is possible to add some candidates in cells so that the puzzle can still be solved.

Pyrrhon

The New Sudoku Players' Forum

Pencilmark only Sudoku