by ghfick » Sat Feb 28, 2026 8:01 pm
Here is a solution path from PhilsFolly. Like the net step, the contradiction2 step is really tough. So the early steps are not for human solvers. Many searches needed to determine contradictions:
Finned swordfish of 6s (r247\c156), fin at r4c4, eliminating 6 from r5c5, r6c6
When each of the 4s in pair r4c3, r6c2 are made true in turn, and then the 3 at r1c3 is made true, there is a contradiction, so 3 can be removed.
When each of the 7s in pair r5c8, r6c9 are made true in turn, and then the 6 at r6c4 is made true, there is a contradiction, so 6 can be removed.
When each of the 6s in pair r56c7 are made true in turn, and then the 1 at r7c1 is made true, there is a contradiction, so 1 can be removed.
When each of the 7s in pair r1c3, r3c1 are made true in turn, and then the 1 at r4c3 is made true, there is a contradiction, so 1 can be removed.
When each of the 7s in pair r1c3, r3c1 are made true in turn, and then the 9 at r2c6 is made true, there is a contradiction, so 9 can be removed.
When each of the 7s in pair r5c8, r6c9 are made true in turn, and then the 1 at r5c3 is made true, there is a contradiction, so 1 can be removed.
When each of the 1s in pair r17c3 are made true in turn, and then the 4 at r9c8 is made true, there is a contradiction, so 4 can be removed.
When each of the 1s in pair r45c5 are made true in turn, and then the 1 at r7c7 is made true, there is a contradiction, so 1 can be removed.
When each of the 1s in pair r7c39 are made true in turn, and then the 4 at r8c8 is made true, there is a contradiction, so 4 can be removed.
When each of the 1s in pair r7c39 are made true in turn, and then the 2 at r1c7 is made true, there is a contradiction, so 2 can be removed.
If 4 is true in r7c3 then the 1 at r1c3 is both true and false, hence 4 is false and can be eliminated
If 4 is true in r8c9 then the 4 at r4c3 is both true and false, hence 4 is false and can be eliminated
When each of the 1s in pair r45c5 are made true in turn, and then the 3 at is made false, there is a contradiction, so r1c7 can be made equal to 3
If 7 is false in r5c8 then the 9 at r9c4 is both true and false, hence 7 must be true in r5c8
If 1 is false in r7c3 then the 1 at r7c9 is both true and false, hence 1 must be true in r7c3
If 7 is false in r1c3 then the 7 at r9c6 is both true and false, hence 7 must be true in r1c3
If 1 is false in r9c7 then the 9 at r5c5 is both true and false, hence 1 must be true in r9c7
4s at r7c79 only ones in box => -4 r7c5.
Finned X-wing of 1s (r16\c29), fin at r6c1, eliminating 1 from r5c2
Since the 9 must be true in either r2c5, r3c5, r5c5 or r8c5, chains beginning with each all show 9 to be false at r2c8
chain1: (9)r2c5 - r1c4 = r1c9 - r2c8
chain2: (9)r3c5 - r1c4 = r1c9 - r2c8
chain3: (9)r5c5 - r6c4 = r6c1 - r3c1 = r2c3 - r2c8
chain4: (9)r8c5 - r8c9 = r9c8 - r2c8
Since the 9 must be true in either r2c5, r3c5, r5c5 or r8c5, chains beginning with each all show 9 to be false at r3c8
chain1: (9)r2c5 - r1c4 = r1c9 - r3c8
chain2: (9)r3c5 - r1c4 = r1c9 - r3c8
chain3: (1)r5c5 = r4c5 - r4c8 = (1-9)r3c8
chain4: (9)r8c5 - r8c9 = r9c8 - r3c8
9s at r89c8 only ones in row/column => -9 r8c9.
Naked triplets of 148 at r234c8 => -8 r89c8
Since the 1 at r1c2 must be either true or false, chains beginning in each case show 1 to be false at r3c1
chain1: (1)r1c2 - r1c9 = r3c8 - r3c1
chain2: (1)r1c2 = (1-9)r1c9 = r2c9 - r2c3 = (9-1)r3c1
1s at r456c1 only ones in row/column => -1 r6c2.
If 9 is false in r3c1 then the 9 at r6c1 is both true and false, hence 9 must be true in r3c1
Naked quads of 1246 at r6c1279 => -2 r6c46
Discontinuous chain: (4=8)r2c8 - (8=1)r1c2, r2c123 - (1)r1c9 = (1-4)r3c8 => -4 r3c8
Bidirectional discontinuous chain: (5)r7c6 = (5)r7c5 - (5=6)r4c5 - (6)r2c5 = (6-5)r2c6 => -5 r2c6 -6 r7c6
Chain with ALS/groups: (4=8)r7c7 - (8)r5c7 = (8)r5c4 - (8)r8c4 = (8)r8c2 - (8)r7c1 = (8)r2c1 - (8=4)r2c8 => -4 r3c7
4s at r3c45 only ones in row/column => -4 r2c5.
Naked triplets of 128 at r3c278 => -2 r3c4
Chain with ALS/groups: (2=8)r3c7 - (8=2)r3c2 - (2=3)r2c3 - (3=2)r4c3 - (2)r6c2 = (2)r6c79 => -2 r5c7
Chain with ALS/groups: (2=3)r2c3 - (3=2)r4c3 - (2)r5c2 = (2-8)r5c4 = (8)r5c7 - (8=2)r3c7 => -2 r2c9, r3c2
Simple chain: (9)r2c5 = (9-4)r8c5 = (4)r3c5 - (4=7)r3c4 - (7=9)r6c4 => -9 r1c4
Simple chain: (9=7)r6c4 - (7=4)r3c4 - (4)r3c5 = (4)r8c5 - (4=3)r8c3 - (3=9)r8c8 => -9 r8c4
Simple discontinuous loop: (1=6)r6c1 - (6=4)r6c7 - (4)r6c2 = (4-3)r4c3 = (3)r4c1 => -1 r4c1
Simple discontinuous loop: (1=6)r6c1 - (6)r6c7 = (6-8)r5c7 = (8-2)r5c4 = (2)r5c2 - (2)r6c2 = (2)r6c9 => -1 r6c9
Simple chain: (5=6)r4c5 - (6)r7c5 = (6)r7c1 - (6=5)r5c1 => -5 r4c1, r5c4
Discontinuous chain: (3)r9c8 = (3-9)r8c8 = (9)r8c5 - (9=7)r247c5 - (7)r7c1 = (7-3)r9c1 => -3 r9c1
Chain with ALS/groups: (8=1)r3c2 - (1)r1c2 = (1-9)r1c9 = (9)r1c6 - (9=7)r247c5 - (7|9=8)r9c6 => -8 r9c2
Naked pairs of 34 at r8c3, r9c2 => -3 r8c2, -4 r8c2
Discontinuous chain: (6=8)r8c2 - (8=1)r3c2 - (1=9)r1c246 - (9)r2c5 = (9-6)r8c5 => -6 r8c5
Chain with ALS/groups: (8=1)r3c2 - (1=9)r1c246 - (9=7)r247c5 - (7=6)r7c179 - (6=8)r8c2 => -8 r2c2
Chain with ALS/groups: (8)r3c8 = (8)r3c2 - (8=6)r8c2 - (6)r6c2 = (6)r6c7 - (6=8)r5c7 => -8 r4c8
8s at r23c8 only ones in row/column => -8 r2c9.
Chain with ALS/groups: (1=9)r1c9 - (9)r1c6 = (9)r2c5 - (9)r8c5 = (9-3)r8c8 = (3)r8c3 - (3=4)r24c3 - (4=1)r4c8 => -1 r3c8, r4c9
stte
