The New Sudoku Players' Forum

Website · by **denis_berthier** » Wed Jan 15, 2025 4:54 am

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Code: Select all: +-------+-------+-------+ ! . . . ! 4 5 6 ! 7 . 9 ! ! . . . ! . 8 9 ! . . . ! ! 6 9 . ! 3 2 . ! . . . ! +-------+-------+-------+ ! . . . ! . . . ! . . 7 ! ! . 3 6 ! . 7 . ! . 9 1 ! ! 7 . 9 ! . . . ! . 2 . ! +-------+-------+-------+ ! 3 6 . ! . . . ! . . . ! ! . 7 2 ! . . 3 ! . 6 . ! ! 9 . 1 ! . . 2 ! . . 3 ! +-------+-------+-------+ ...4567.9....89...69.32............7.36.7..917.9....2.36........72..3.6.9.1..2..3

Code: Select all: Resolution state after Singles and whips[1]: +----------------------+----------------------+----------------------+ ! 128 128 38 ! 4 5 6 ! 7 138 9 ! ! 145 145 3457 ! 17 8 9 ! 123456 1345 2456 ! ! 6 9 4578 ! 3 2 17 ! 1458 1458 458 ! +----------------------+----------------------+----------------------+ ! 12458 12458 458 ! 125689 13469 1458 ! 34568 3458 7 ! ! 2458 3 6 ! 258 7 458 ! 458 9 1 ! ! 7 1458 9 ! 1568 1346 1458 ! 34568 2 4568 ! +----------------------+----------------------+----------------------+ ! 3 6 458 ! 15789 149 14578 ! 124589 14578 2458 ! ! 458 7 2 ! 1589 149 3 ! 14589 6 458 ! ! 9 458 1 ! 5678 46 2 ! 458 4578 3 ! +----------------------+----------------------+----------------------+ 194 candidates.

by **Cenoman** » Wed Jan 15, 2025 8:38 pm

As a start, a solution in four steps, among which tridagon and UR.

Code: Select all: +-------------------------+-------------------------+--------------------------+ | 128 128 38 | 4 5 6 | 7 138 9 | | 145 145 3457 | z17 8 9 | 26 1345 26 | | 6 9 4578 | 3 2 7-1 |Zb1458 1458 458 | +-------------------------+-------------------------+--------------------------+ | B12458 B12458 458* | 69 369 C1458 | b36 458* 7 | | 458* 3 6 | 2 7 458 | b458* 9 1 | | 7 A1458* 9 | 1568 1346 1458 | b34568 2 a4568* | +-------------------------+-------------------------+--------------------------+ | 3 6 458* | 15789 149 14578 | Y124589 Xw14578* 2458 | | 458* 7 2 | 1589 149 3 | Y14589 6 458* | | 9 458* 1 | y5678 46 2 | b458* x4578 3 | +-------------------------+-------------------------+--------------------------+

1. Tridagon (458)b4679 (*) having four guardians (1r6c2, 6r6c9, 17r7c8)
(6)r6c9 - (6=34581)r34569c7
(1)r6c2 - r4c12 = (1)r4c6
(7)r7c8 - r9c8 = r9c4 - (7=1)r2c4
(1)r7c8 - r78c7 = (1)r3c7
=> -1 r3c6; lcls, 7 placements

Code: Select all: +--------------------+-----------------------+-------------------------+ | 12* 12* 3 | 4 5 6 | 7 8 9 | | 45 45 7 | 1 8 9 | 26 3 26 | | 6 9 8 | 3 2 7 | 145 145 45 | +--------------------+-----------------------+-------------------------+ | 12* 12+8* 45 | 69 369 18 | 36 45 7 | | 458 3 6 | 2 7 458 | 458 9 1 | | 7 1458 9 | 568 1346 1458 | 34568 2 4568 | +--------------------+-----------------------+-------------------------+ | 3 6 45 | 5789 149 1458 | 124589 1457 2458 | | 458 7 2 | 589 149 3 | 14589 6 458 | | 9 458 1 | 5678 46 2 | 458 457 3 | +--------------------+-----------------------+-------------------------+

2. UR(12)r14c12, using single internal => +8 r4c2; lcls, 7 placements

Code: Select all: +-----------------+---------------------+-----------------------+ | 1 2 3 | 4 5 6 | 7 8 9 | | 45 45 7 | 1 8 9 | 26 3 26 | | 6 9 8 | 3 2 7 | 145 145 45 | +-----------------+---------------------+-----------------------+ | 2 8 45* | 69 369 1 | 36 45* 7 | | 45 3 6 | 2 7 458^ | 458^ 9 1 | | 7 1 9 | 56-8 346 458 | 34568 2 68 | +-----------------+---------------------+-----------------------+ | 3 6 45* | 5789 149 45-8 | 124589 1457 28 | | 8 7 2 | 59 149 3 | 1459 6 45 | | 9 45* 1 | 5678^ 46 2 | 458^ 7-45 3 | +-----------------+---------------------+-----------------------+

3. Remote Pair (45)r4c38, b7p38 => -45 r9c8
4. Skyscraper (8): r5c6 = r5c7 - r9c7 = r9c4 => -8 r6c4, r7c6; lclste

Added. Solution w/o uniqueness.
After step #1, the rating is lowered to skfr 6.6, but the end is'nt that easy.
This puzzle is a nice example of a solution simplified by uniqueness.
After step #1:

Code: Select all: +--------------------+-----------------------+-------------------------+ | 12 12 3 | 4 5 6 | 7 8 9 | | 45 45 7 | 1 8 9 | 26 3 26 | | 6 9 8 | 3 2 7 | 145 145 d45 | +--------------------+-----------------------+-------------------------+ | 12 128* C45 | 69 369 18* | 36 Ba45 7 | | b458 3 6 | 2 7 F458 |Aa45-8* 9 1 | | 7 1458 9 | G56-8 1346 F1458 | 34568* 2 G68*-45 | +--------------------+-----------------------+-------------------------+ | 3 6 D45 | 5789 149 E1458 | 124589 1457 2458 | | c458 7 2 | 589 149 3 | 14589 6 d458 | | 9 458* 1 | 5678* 46 2 | 458* 457 3 | +--------------------+-----------------------+-------------------------+

2. (8): r9c4 =' [r4c6 = r4c2 - r9c2 '= r9c7 - r56c7 = r6c7] => -8 r6c4 (*)
3. ALS W-Wing (45=8)b6b24 - r5c1 = r8c1 - (8=45)r38c9 => -45 r6c9
4. (5)r5c7 = r4c8 - r4c3 = r7c3 - r7c6 = r56c6 - (5=68)r6c49 => -8 r5c7; lcls

Code: Select all: +-------------------+----------------------+-------------------------+ | 12 12 3 | 4 5 6 | 7 8 9 | | 45 45 7 | 1 8 9 | 26 3 26 | | 6 9 8 | 3 2 7 | 145 145 45 | +-------------------+----------------------+-------------------------+ | 12 128 45#^ | 69 369 18 | 36 45#^ 7 | | 458 3 6 | 2 7 458 | 45# 9 1 | | 7 145 9 | 56 1346 145 | 368 2 68 | +-------------------+----------------------+-------------------------+ | 3 6 45*#^| 78-59 149* 145* | 1289-45 17-45 28-45 | | 458*# 7 2 | 589 149* 3 | 19-458 6 45-8*# | | 9 45-8^ 1 | 5678 46 2 | 458# 7-45 3 | +-------------------+----------------------+-------------------------+

5. MSLS; 7 cells (*): r7c356, r8c1459; 7 links: 45r78, 8r8, 19b8 => -59 r7c4, -45 r7c789, -458 r8c7; HP(45)r38c9 => -8 r8c9
6. 7-link bivalue oddagon (45)r48,c37,b679 (#), having two guardians: (8): r8c1 = r9c7 => -8 r9c2; lcls, 9 placements
7. Remote Pair (45)r4c38, b7p38 (^) => -45 r9c8; ste

Website · by **denis_berthier** » Thu Jan 16, 2025 5:37 am

Cenoman wrote:As a start, a solution in four steps, among which tridagon and UR.
Code: Select all
+-------------------------+-------------------------+--------------------------+ | 128 128 38 | 4 5 6 | 7 138 9 | | 145 145 3457 | z17 8 9 | 26 1345 26 | | 6 9 4578 | 3 2 7-1 |Zb1458 1458 458 | +-------------------------+-------------------------+--------------------------+ | B12458 B12458 458* | 69 369 C1458 | b36 458* 7 | | 458* 3 6 | 2 7 458 | b458* 9 1 | | 7 A1458* 9 | 1568 1346 1458 | b34568 2 a4568* | +-------------------------+-------------------------+--------------------------+ | 3 6 458* | 15789 149 14578 | Y124589 Xw14578* 2458 | | 458* 7 2 | 1589 149 3 | Y14589 6 458* | | 9 458* 1 | y5678 46 2 | b458* x4578 3 | +-------------------------+-------------------------+--------------------------+

The question is, how do you reach this starting point, where many candidates not eliminated by W1 or Basics are already missing?

by **eleven** » Thu Jan 16, 2025 10:45 pm

denis_berthier wrote:
Cenoman wrote:The question is, how do you reach this starting point, where many candidates not eliminated by W1 or Basics are already missing?

The hidden pair 26r2c79 (naked quad 13458) in box 3 and the hidden triple 369 (naked quint 12458) in row 4 are basics.

Website · by **denis_berthier** » Fri Jan 17, 2025 12:40 pm

eleven wrote:
denis_berthier wrote:
Cenoman wrote:The question is, how do you reach this starting point, where many candidates not eliminated by W1 or Basics are already missing?

The hidden pair 26r2c79 (naked quad 13458) in box 3 and the hidden triple 369 (naked quint 12458) in row 4 are basics.

OK. I had missed them because I grant Deadly Patterns higher priorities. In this puzzle, it's better to look for them later.
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Website · by **denis_berthier** » Fri Jan 17, 2025 1:01 pm

Cenoman wrote:This puzzle is a nice example of a solution simplified by uniqueness.

That's why I chose it among those with a tridagon.
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