The New Sudoku Players' Forum

Website · by **denis_berthier** » Fri Jun 03, 2022 6:38 am

.
One more puzzle with this pattern:

Code: Select all: +-------+-------+-------+ ! X . X ! . . . ! . . . ! ! . X . ! . . . ! . . . ! ! X . X ! . . . ! . . . ! +-------+-------+-------+ ! . . . ! . X X ! X X . ! ! . . . ! X X . ! . X X ! ! . . . ! X . . ! . . X ! +-------+-------+-------+ ! . . . ! X . . ! . . X ! ! . . . ! X X . ! . X X ! ! . . . ! . X X ! X X . ! +-------+-------+-------+

Slightly harder:

Code: Select all: +-------+-------+-------+ ! 1 . 8 ! . . . ! . . . ! ! . 9 . ! . . . ! . . . ! ! 4 . 2 ! . . . ! . . . ! +-------+-------+-------+ ! . . . ! . 3 8 ! 2 4 . ! ! . . . ! 6 1 . ! . 8 9 ! ! . . . ! 7 . . ! . . 1 ! +-------+-------+-------+ ! . . . ! 8 . . ! . . 7 ! ! . . . ! 4 5 . ! . 1 8 ! ! . . . ! . 2 6 ! 4 3 . ! +-------+-------+-------+ 1.8.......9.......4.2..........3824....61..89...7....1...8....7...45..18....2643. # 96114 FBTXYK C25.m/S2.d SER = 7.3

by **eleven** » Fri Jun 03, 2022 9:17 am

Code: Select all: *--------------------------------------------------------------* | 1 d367 8 | e23 67 e49 | 5 679 e24 | | c367 9 c3567 | 23 678 145 | 18 67 24 | | 4 567 2 | 59 678 159 | 18 679 3 | |-----------------------+-------------------+------------------| | 79 157 1579 | 59 3 8 | 2 4 6 | | b23 2345 345 | 6 1 a25 | 7 8 9 | | 2689 268 b69 | 7 4 fa29 | 3 5 1 | |-----------------------+-------------------+------------------| | 5 14 14 | 8 9 3 | 6 2 7 | | 236 236 b36 | 4 5 7 | 9 1 8 | | 789 78 79 | 1 2 6 | 4 3 5 | *--------------------------------------------------------------*

(5=29)r56c6 - (2|9) = 3r5c1 & 63r68c3 - 3r2c13 = r1c2 - (3=249)r1c496 - (9=2)r6c6 => -2r5c6, stte

Website · by **denis_berthier** » Sun Jun 05, 2022 4:07 am

.

Code: Select all: Resolution state after Singles and whips[1]: +----------------+----------------+----------------+ ! 1 367 8 ! 239 67 49 ! 5 679 24 ! ! 367 9 3567 ! 235 678 145 ! 18 67 24 ! ! 4 567 2 ! 59 678 159 ! 18 679 3 ! +----------------+----------------+----------------+ ! 79 157 1579 ! 59 3 8 ! 2 4 6 ! ! 23 2345 345 ! 6 1 25 ! 7 8 9 ! ! 2689 268 69 ! 7 4 29 ! 3 5 1 ! +----------------+----------------+----------------+ ! 5 14 14 ! 8 9 3 ! 6 2 7 ! ! 236 236 36 ! 4 5 7 ! 9 1 8 ! ! 789 78 79 ! 1 2 6 ! 4 3 5 ! +----------------+----------------+----------------+ 105 candidates

The puzzle is in Z4:

Hidden Text: Show

It has 1-step solutions, but that requires long chains. Here are two with braids[8]:

Code: Select all: braid[8]: r6c6{n2 n9} - r1c6{n9 n4} - r2n4{c6 c9} - r2n2{c9 c4} - r5c1{n2 n3} - r2n3{c1 c3} - r6c3{n9 n6} - r8c3{n6 .} ==> r5c6≠2 (same elimination as eleven, different pattern) stte

Code: Select all: braid[8]: r1c6{n9 n4} - r2n4{c6 c9} - r2n2{c9 c4} - r6c3{n9 n6} - c6n2{r6 r5} - r5c1{n2 n3} - r2n3{c1 c3} - r8c3{n6 .} ==> r6c6≠9 stte

As braids are not a very likeable pattern, one may prefer whips, but that requires still longer ones:

Code: Select all: whip[10]: c6n9{r3 r6} - r1c6{n9 n4} - r2n4{c6 c9} - r2n2{c9 c4} - c4n5{r2 r4} - r5c6{n5 n2} - r5c1{n2 n3} - r2n3{c1 c3} - r8c3{n3 n6} - r6c3{n6 .} ==> r3c4≠9 stte

Code: Select all: whip[11]: r1c6{n9 n4} - r2n4{c6 c9} - r2n2{c9 c4} - c4n3{r2 r1} - c4n9{r1 r3} - r4c4{n9 n5} - r5c6{n5 n2} - r5c1{n2 n3} - c2n3{r5 r8} - r8c3{n3 n6} - r6c3{n6 .} ==> r6c6≠9 stte

I prefer 2-step solutions with shorter and simpler chains:

Code: Select all: biv-chain[5]: r8c3{n3 n6} - r6c3{n6 n9} - b5n9{r6c6 r4c4} - r3c4{n9 n5} - b1n5{r3c2 r2c3} ==> r2c3≠3 biv-chain[6]: r5c1{n2 n3} - r2n3{c1 c4} - b2n2{r2c4 r1c4} - r1c9{n2 n4} - r1c6{n4 n9} - r6c6{n9 n2} ==> r5c6≠2, r6c1≠2, r6c2≠2 stte

OR:

Code: Select all: biv-chain[5]: r8c3{n3 n6} - r6c3{n6 n9} - b5n9{r6c6 r4c4} - r3c4{n9 n5} - b1n5{r3c2 r2c3} ==> r2c3≠3 biv-chain[6]: r1c6{n9 n4} - b3n4{r1c9 r2c9} - r2n2{c9 c4} - r2n3{c4 c1} - r5c1{n3 n2} - b5n2{r5c6 r6c6} ==> r6c6≠9 stte

Note that while the simplest-first solution (in Z4) uses chains with z-candidates, the above two solutions use only elementary bivalue-chains.

Same pattern but SER 7.3