The New Sudoku Players' Forum

[marek stefanik]

So, would it make it clearer if I added a line saying that the link 7# = (3|5)&249# is valid because of the two previous observations?
249b7# \ r7c16 is obifish notation: each of 249 appears both in b7 and # and the base sets are covered by r7c16 (rank1), so r7c6 can be eliminated (it would leave us with two base sets and one cover set, so negative rank, ie. contra.). I like it more than leaving say r7c23 as fins.

Marek

[yzfwsf]

At this point, the skfr of this puzzle is 9.3 and YZF_Sudoku finds a way through with complex nets.
However, it is an absolute Tal's forest and I cannot recommend this approach to anyone solving the puzzle manually (huge respect to totuan for finding a way).
Instead, one can relabel in hope to reduce the difficulty (r1 gives 7.6, but b4 gives 8.9) or consider the remaining combinations of TH guardians (mostly) one by one.
Marek

My solver now implements a forced chain of various impossible patterns.

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Locked Candidates 2 (Claiming): 8 in r8 => r7c6<>8,r9c4<>8,r9c6<>8
Uniqueness External Test 2/4: 58 in r48c46 => r69c1<>5
2-String Kite: 5 in r6c6,r8c1 connected by b4p19 => r8c6 <> 5
Grouped AIC Type 2: (9=3)r8c7 - r12c7 = (3-6)r2c8 = 6r9c8 => r9c8<>9
Almost Locked Set XY-Wing: A=r4c1258{24579}, B=r4c12568{245789}, C=r8c1567{34589}, X,Y=5, 8, Z=249 =>  r4c4<>2 r4c4<>4 r4c4<>9
Triplet Oddagon Forcing Chain: Each true guardian of Triplet Oddagon will all lead To: r1c7<>2,r1c7<>9
 3r2c1 - 3r1c3 = 3r1c7
 7r2c1 - 7r12c3 = 7r6c3 - 7r1c3,r6c7 = 7r1c7
 7r6c1 - 7r6c7 = 7r12c7 - (7=492)r1c249
 5r6c6 - (5=24897)r4c24568 - 7r6c7 = 7r12c7 - (7=492)r1c249
Impossible Pattern(249) Forcing Chain: Each true guardian of Impossible Pattern will all lead To: r6c3<>2,r6c3<>4,r6c3<>9
 5r4c6 - 5r6c6 = 5r6c3
 8r4c6 - (8=5)r4c4 - 5r6c6 = 5r6c3
 5r6c3
 7r6c3
 7r7c6 - (7=23598)r9c13456 - 5r9c3 = 5r6c3
Triplet Oddagon Forcing Chain: Each true guardian of Triplet Oddagon will all lead To: r79c9<>9
 3r2c1 - 3r1c3 = 3r1c7 - (3=9)r8c7
 7r2c1 - 7r4c1 = 7r4c8 - (7=39)b9p24
 7r6c1 - 7r4c1 = 7r4c8 - (7=39)b9p24
 5r6c6 - (5=24897)r4c24568 - (7=39)b9p24
Uniqueness External Test 2/4: 19 in r36c79 => r3c7<>9
Impossible Pattern(249) Forcing Chain: Each true guardian of Impossible Pattern will all lead To: r7c8<>7
 7r6c1 - 7r4c1 = 7r4c8
 5r6c6 - (5=24897)r4c24568
 7r7c6
 3r9c1 - 3r7c13 = 3r7c8
 3r9c5 - (3=687)b9p389
Naked Pair: in r7c8,r8c7 => r9c8<>3,
2-String Kite: 3 in r1c3,r7c8 connected by b3p15 => r7c3 <> 3
Hidden Rectangle: 67 in r29c89 => r2c9 <> 7
Almost Locked Set XY-Wing: A=r1c249{2479}, B=r357c3{2489}, C=r7c9{78}, X,Y=7, 8, Z=249 =>  r1c3<>2 r1c3<>4 r1c3<>9
Naked Pair: in r1c3,r1c7 => r1c9<>7,
UR Forcing Chain: Each true guardian of UR 37{r12c37} will all lead to: r2c8,r9c9<>6
 2r2c3 - (2=498)r357c3 - (8=14796)r12367c9
 4r2c3 - (4=298)r357c3 - (8=14796)r12367c9
 9r2c3 - (9=248)r357c3 - (8=14796)r12367c9
 2r2c7 - (2=1496)b3p3679
 9r2c7 - (9=46)r12c9
Hidden Single: 6 in r2 => r2c9=6
Hidden Single: 6 in r9 => r9c8=6
Locked Candidates 1 (Pointing): 7 in b9 => r6c9<>7
Impossible Pattern(249) Forcing Chain: Each true guardian of Impossible Pattern will all lead To: r8c1<>3
 3r2c8 - 3r7c8 = 3r8c7
 7r2c8 - 7r4c8 = (7-5)r4c1 = 5r8c1
 7r6c1 - (7=5)r6c3 - 5r4c1 = 5r8c1
 3r7c1
 7r7c6 - (7=2395)r9c1456 - 5r8c4 = 5r8c1
 3r9c1
 5r9c4 - 5r8c4 = 5r8c1
UR Forcing Chain: Each true guardian of UR 59{r89c16} will all lead to: r8c6<>9
 4r8c1 - (4=398)r8c567
 4r8c6
 8r8c6
 2r9c1 - (2=34895)b8p45678 - (5=8)r4c4 - 8r8c4 = 8r8c6
 3r9c1 - 3r7c1 = (3-9)r7c8 = 9r8c7
 2r9c6 - (2=395)r9c145 - (5=8)r4c4 - 8r8c4 = 8r8c6
 (7-5)r9c6 = 5r89c4 - (5=8)r4c4 - 8r8c4 = 8r8c6
Whip[11]: Supposing 4r4c6 will result in 4 to disappear in Box 3 => r4c6<>4
4r4c6 - 8r4(c6=c4) - 5r4(c4=c1) - 5r8(c1=c4) - 4c4(r8=r1) - 2r1(c4=c2) - r4c2(2=9) - r4c5(9=2) - r3c5(2=9) - r3c3(9=4) - 4r5(c3=c8) - 4b3(p5=.)
Whip[10]: Supposing 9r8c1 will result in 3 to disappear in Box 8 => r8c1<>9
9r8c1 - r8c7(9=3) - r8c5(3=4) - r8c6(4=8) - r8c4(8=5) - 5c1(r8=r4) - 7r4(c1=c8) - 4r4(c8=c2) - r7c2(4=2) - r9c1(2=3) - 3b8(p8=.)
Whip[12]: Supposing 9r4c6 will result in 9 to disappear in Box 9 => r4c6<>9
9r4c6 - 8r4(c6=c4) - 5r4(c4=c1) - r8c1(5=4) - 4r7(c3=c6) - r2c6(4=2) - 2r1(c4=c2) - r4c2(2=4) - 4c5(r4=r3) - r3c3(4=9) - 9r5(c3=c8) - 9r2(c8=c7) - 9b9(p4=.)
Region Forcing Chain: Each 9 in c6 true in turn will all lead to: r2c7<>9
 9r2c6
 9r6c6 - 9r6c9 = 9r13c9
 9r7c6 - 9r7c8 = 9r8c7
 9r9c6 - 9r8c45 = 9r8c7
UR Forcing Chain: Each true guardian of UR 37{r12c37} will all lead to: r2c1<>2
 2r2c3
 4r2c3 - (4=92)b1p29
 9r2c3 - (9=42)b1p29
 2r2c7
Impossible Pattern(249) Forcing Chain: Each true guardian of Impossible Pattern will all lead To: r2c6<>2
 3r2c8 - (3=72)r12c7
 7r2c8 - (7=32)r12c7
 (1-2)r3c7 = 2r2c78
 5r6c6 - (5=82)r4c46
 1r6c9 - (1=34792)b3p13459
Impossible Pattern(249) Forcing Chain: Each true guardian of Impossible Pattern will all lead To: r2c8<>9
 3r2c8
 7r2c8
 1r3c7 - (1=49)r13c9
 5r6c6 - 5r6c3 = 5r4c1 - (5=4)r8c1 - 4r7c123 = 4r7c6 - (4=9)r2c6
 7r7c6 - (7=8)r7c9 - (8=492)r357c3 - 2r2c3 = 2r2c78 - (2=149)b3p379
Locked Candidates 1 (Pointing): 9 in b3 => r6c9<>9
Whip[9]: Supposing 2r2c3 will result in all candidates in cell r5c3 being impossible => r2c3<>2
2r2c3 - 2r1(c2=c4) - 2r3(c5=c7) - 1r3(c7=c9) - r6c9(1=4) - 4r1(c9=c2) - r3c3(4=9) - r3c5(9=4) - 4r4(c5=c1) - r5c3(4=.)
Locked Candidates 2 (Claiming): 2 in r2 => r3c7<>2
Naked Single: r3c7=1
Hidden Single: 1 in r6 => r6c9=1
Locked Candidates 1 (Pointing): 4 in b6 => r2c8<>4
Whip[13]: Supposing 7r2c1 will result in 2 to disappear in Row 5 => r2c1<>7
7r2c1 - 7c3(r1=r6) - 5c3(r6=r9) - r8c1(5=4) - 4r7(c3=c6) - 4r2(c6=c3) - 4c2(r1=r4) - 4c5(r4=r3) - 2r3(c5=c3) - 2r1(c2=c4) - r9c4(2=9) - 9r8(c5=c7) - r6c7(9=2) - 2r5(c8=.)
Locked Candidates 2 (Claiming): 7 in c1 => r6c3<>7
Naked Single: r6c3=5
Hidden Single: 5 in c1 => r8c1=5
Locked Candidates 1 (Pointing): 4 in b7 => r7c6<>4
Hidden Pair: 58 in r4c4,r4c6 => r4c6<>2
Uniqueness Test 7: 37 in r12c37; 2*biCell + 1*conjugate pairs(7c3) => r2c7 <> 3
Impossible Pattern(249) Forcing Chain: Each true guardian of Impossible Pattern will all lead To: r2c3<>3
 3r2c8
 7r2c8 - 7r12c7 = 7r6c7 - 7r6c1 = 3r2c1
 7r6c7 - 7r6c1 = 3r2c1
 7r6c8 - 7r6c1 = 3r2c1
X-Wing:3r27\c18  => r9c1<>3
WXYZ-Wing: 2349 in r7c128,r9c1,Pivot Cell Is r7c1 => r7c3<>9
Grouped AIC Type 2: (9=2)r9c1 - r7c123 = (2-7)r7c6 = (7-5)r9c6 = 5r9c4 => r9c4<>9
Grouped AIC Type 2: (9=2)r9c1 - r7c123 = (2-7)r7c6 = 7r9c6 => r9c6<>9
Cell Forcing Chain: Each candidate in  r6c6 true in turn will all lead to: r2c1<>9
 2r6c6 - 2r7c6 = 2r7c123 - (2=9)r9c1
 4r6c6 - (4=9)r2c6
 9r6c6 - (9=273)r126c7 - 3r2c8 = 3r2c1
Impossible Pattern(249) Forcing Chain: Each true guardian of Impossible Pattern will all lead To: r2c7<>7
 3r2c8 - (3=497)r2c136
 7r2c8
 7r7c6 - (7=8)r7c9 - (8=2497)r2357c3
Naked Single: r2c7=2
AIC Type 2: (4=3)r2c1 - (3=7)r2c8 - r4c8 = 7r4c1 => r4c1<>4
XY-Chain with Triplet Oddagon: 7r24c8 = r4c1 - r6c1 = 3r2c1 - (3=7)r2c8 => r6c8<>7
Impossible Pattern(249) Forcing Chain: Each true guardian of Impossible Pattern will all lead To: r2c1<>3,r2c36,r67c1,r1c2,r3c3<>4
 7r6c1 - 7r6c7 = (7-3)r1c7 = 3r2c8 - (3=4)r2c1
 7r7c6 - (7=2593)r9c1456 - 3r9c3 = 3r7c1 - (3=4)r2c1
Hidden Single: 3 in r2 => r2c8=3
Hidden Single: 3 in r1 => r1c3=3
Hidden Single: 7 in r1 => r1c7=7
Hidden Single: 4 in r2 => r2c1=4
Hidden Single: 7 in r2 => r2c3=7
Full House: r2c6=9
Hidden Single: 7 in r6 => r6c1=7
Hidden Single: 7 in r4 => r4c8=7
Hidden Single: 3 in r7 => r7c1=3
Hidden Single: 3 in r9 => r9c5=3
Hidden Single: 3 in r8 => r8c7=3
Full House: r6c7=9
Hidden Single: 9 in c8 => r7c8=9
Avoidable Rectangle Type 1: 19 in r36c79 => r3c9 <> 9
stte


Now there is no need to use brute force to solve this puzzle.

[yzfwsf]

17 Cells Impossible Pattern:

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.1.1....1.....1.1.....1.....1..1......11...1.1........11...1............1..1.....

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.1. 1.. ..1
... ..1 .1.
... .1. ...
.1. .1. ...
..1 1.. .1.
1.. ... ...
11. ..1 ...
... ... ...
1.. 1.. ...

[denis_berthier]

.
Great to have a solution, finally.
There's only 1 free cell in your 17-cell pattern; it can't appear in a puzzle in a non-degenerate form - which makes it very hard to find.

Code: Select all

(browse-k-digit-pattern 3 ".1.1....1.....1.1.....1.....1..1......11...1.1........11...1............1..1....." TRUE)
   1 cells free for pattern digits: (r8c7)
   1 rows with no cell in the pattern: (r8)
   1 columns with no-cell in the pattern: (c7)
   1 blocks with no-cell in the pattern: (b9)
   0 bands with no-cell in the pattern: ()
   0 stacks with no-cell in the pattern: ()

     +-------+-------+-------+
     ! . X . ! X . . ! . . X !
     ! . . . ! . . X ! . X . !
     ! . . . ! . X . ! . . . !
     +-------+-------+-------+
     ! . X . ! . X . ! . . . !
     ! . . X ! X . . ! . X . !
     ! X . . ! . . . ! . . . !
     +-------+-------+-------+
     ! X X . ! . . X ! . . . !
     ! . . . ! . . . ! o . . !
     ! X . . ! X . . ! . . . !
     +-------+-------+-------+