Oct 24 - Super Hard
Puzzle Copyright © Kevin Stone
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Reasoning
R1C7 is the only square in row 1 that can be <1>
R2C8 is the only square in row 2 that can be <7>
R4C2 is the only square in row 4 that can be <1>
R5C6 is the only square in row 5 that can be <1>
R6C5 is the only square in row 6 that can be <7>
R7C6 is the only square in row 7 that can be <9>
R8C8 is the only square in row 8 that can be <1>
R9C9 is the only square in row 9 that can be <7>
R9C5 is the only square in column 5 that can be <4>
Intersection of row 6 with block 4. The value <8> only appears in one or more of squares R6C1, R6C2 and R6C3 of row 6. These squares are the ones that intersect with block 4. Thus, the other (non-intersecting) squares of block 4 cannot contain this value.
R5C1 - removing <8> from <3568> leaving <356>
R5C2 - removing <8> from <3589> leaving <359>
Intersection of row 8 with block 8. The value <2> only appears in one or more of squares R8C4, R8C5 and R8C6 of row 8. These squares are the ones that intersect with block 8. Thus, the other (non-intersecting) squares of block 8 cannot contain this value.
R7C4 - removing <2> from <27> leaving <7>
R8C2 is the only square in row 8 that can be <7>
Intersection of row 9 with block 7. The value <8> only appears in one or more of squares R9C1, R9C2 and R9C3 of row 9. These squares are the ones that intersect with block 7. Thus, the other (non-intersecting) squares of block 7 cannot contain this value.
R8C3 - removing <8> from <3568> leaving <356>
Intersection of block 8 with row 8. The values <238> only appears in one or more of squares R8C4, R8C5 and R8C6 of block 8. These squares are the ones that intersect with row 8. Thus, the other (non-intersecting) squares of row 8 cannot contain these values.
R8C3 - removing <3> from <356> leaving <56>
R8C7 - removing <3> from <356> leaving <56>
Intersection of block 9 with column 7. The value <6> only appears in one or more of squares R7C7, R8C7 and R9C7 of block 9. These squares are the ones that intersect with column 7. Thus, the other (non-intersecting) squares of column 7 cannot contain this value.
R2C7 - removing <6> from <4569> leaving <459>
R6C7 - removing <6> from <356> leaving <35>
R2C4 is the only square in row 2 that can be <6>
Squares R6C7<35>, R8C7<56> and R9C7<36> in column 7 form a comprehensive naked triplet. These 3 squares can only contain the 3 possibilities <356>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the column.
R2C7 - removing <5> from <459> leaving <49>
R4C7 - removing <5> from <459> leaving <49>
Squares R3C2 and R3C9 in row 3 and R5C2 and R5C9 in row 5 form a Simple X-Wing pattern on possibility <9>. All other instances of this possibility in columns 2 and 9 can be removed.
R1C9 - removing <9> from <59> leaving <5>
R2C2 - removing <9> from <4589> leaving <458>
R1C1 can only be <3>
R7C9 can only be <2>
R3C6 is the only square in row 3 that can be <3>
R8C5 is the only square in row 8 that can be <3>
Squares R5C2 and R5C8 in row 5 and R7C2 and R7C8 in row 7 form a Simple X-Wing pattern on possibility <3>. All other instances of this possibility in columns 2 and 8 can be removed.
R6C2 - removing <3> from <358> leaving <58>
R6C8 - removing <3> from <356> leaving <56>
Squares R4C3 (XY), R4C5 (XZ) and R1C3 (YZ) form an XY-Wing pattern on <2>. All squares that are buddies of both the XZ and YZ squares cannot be <2>.
R1C5 - removing <2> from <29> leaving <9>
R1C3 can only be <2>
Squares R5C1 (XY), R4C3 (XZ) and R5C9 (YZ) form an XY-Wing pattern on <9>. All squares that are buddies of both the XZ and YZ squares cannot be <9>.
R5C2 - removing <9> from <359> leaving <35>
R4C7 - removing <9> from <49> leaving <4>
R2C7 can only be <9>
R3C9 can only be <6>
R3C8 can only be <4>
R5C9 can only be <9>
R2C2 is the only square in row 2 that can be <4>
R3C2 is the only square in row 3 that can be <9>
R4C3 is the only square in row 4 that can be <9>
R7C1 is the only square in row 7 that can be <4>
R6C2 is the only square in column 2 that can be <8>
Squares R3C1 and R5C1 in column 1 and R3C4 and R5C4 in column 4 form a Simple X-Wing pattern on possibility <5>. All other instances of this possibility in rows 3 and 5 can be removed.
R5C2 - removing <5> from <35> leaving <3>
R5C5 - removing <5> from <258> leaving <28>
R5C8 - removing <5> from <2356> leaving <236>
R7C2 can only be <5>
R7C8 can only be <3>
R8C3 can only be <6>
R9C7 can only be <6>
R8C7 can only be <5>
R6C3 can only be <5>
R9C1 can only be <8>
R6C7 can only be <3>
R9C3 can only be <3>
R3C1 can only be <5>
R3C4 can only be <8>
R5C1 can only be <6>
R2C3 can only be <8>
R8C4 can only be <2>
R2C6 can only be <2>
R5C8 can only be <2>
R5C4 can only be <5>
R5C5 can only be <8>
R4C8 can only be <5>
R6C8 can only be <6>
R8C6 can only be <8>
R2C5 can only be <5>
R4C5 can only be <2>
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