Jul 20 - Super Hard
Puzzle Copyright © Kevin Stone
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Reasoning
R3C7 is the only square in row 3 that can be <4>
R7C8 is the only square in row 7 that can be <1>
R7C4 is the only square in row 7 that can be <2>
Intersection of column 4 with block 5. The values <35> only appears in one or more of squares R4C4, R5C4 and R6C4 of column 4. These squares are the ones that intersect with block 5. Thus, the other (non-intersecting) squares of block 5 cannot contain these values.
R4C5 - removing <3> from <237> leaving <27>
R5C5 - removing <3> from <23467> leaving <2467>
Squares R1C3<567>, R2C2<567>, R3C1<37> and R3C2<367> in block 1 form a comprehensive naked quad. These 4 squares can only contain the 4 possibilities <3567>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the block.
R2C3 - removing <567> from <12567> leaving <12>
R3C3 - removing <367> from <12367> leaving <12>
Squares R5C1 and R7C1 in column 1 and R5C9 and R7C9 in column 9 form a Simple X-Wing pattern on possibility <5>. All other instances of this possibility in rows 5 and 7 can be removed.
R5C2 - removing <5> from <357> leaving <37>
R7C2 - removing <5> from <35678> leaving <3678>
R7C3 - removing <5> from <34567> leaving <3467>
R5C4 - removing <5> from <356> leaving <36>
R7C7 - removing <5> from <3578> leaving <378>
R5C8 - removing <5> from <2579> leaving <279>
Squares R2C2 and R8C2 in column 2 and R2C8 and R8C8 in column 8 form a Simple X-Wing pattern on possibility <5>. All other instances of this possibility in rows 2 and 8 can be removed.
R8C3 - removing <5> from <345> leaving <34>
R2C7 - removing <5> from <2567> leaving <267>
R8C7 - removing <5> from <3589> leaving <389>
Squares R7C9 (XY), R8C8 (XZ) and R3C9 (YZ) form an XY-Wing pattern on <9>. All squares that are buddies of both the XZ and YZ squares cannot be <9>.
R3C8 - removing <9> from <279> leaving <27>
R3C9 is the only square in row 3 that can be <9>
Squares R5C1<357>, R5C2<37> and R5C9<57> in row 5 form a comprehensive naked triplet. These 3 squares can only contain the 3 possibilities <357>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the row.
R5C4 - removing <3> from <36> leaving <6>
R5C5 - removing <7> from <2467> leaving <246>
R5C6 - removing <7> from <479> leaving <49>
R5C8 - removing <7> from <279> leaving <29>
R3C4 can only be <8>
R6C4 can only be <5>
R4C4 can only be <3>
R3C2 is the only square in row 3 that can be <6>
R3C1 is the only square in row 3 that can be <3>
R5C2 is the only square in row 5 that can be <3>
R7C3 is the only square in row 7 that can be <6>
R7C7 is the only square in row 7 that can be <3>
R7C6 is the only square in row 7 that can be <4>
R5C6 can only be <9>
R5C8 can only be <2>
R4C6 can only be <7>
R5C5 can only be <4>
R3C8 can only be <7>
R3C6 can only be <1>
R2C8 can only be <5>
R4C5 can only be <2>
R2C2 can only be <7>
R8C8 can only be <9>
R1C7 can only be <6>
R3C3 can only be <2>
R6C6 can only be <8>
R6C5 can only be <1>
R8C7 can only be <8>
R1C5 can only be <7>
R2C7 can only be <2>
R2C5 can only be <6>
R7C2 can only be <8>
R1C3 can only be <5>
R2C3 can only be <1>
R8C2 can only be <5>
R7C1 can only be <7>
R8C5 can only be <3>
R9C7 can only be <7>
R9C3 can only be <3>
R6C7 can only be <9>
R7C9 can only be <5>
R4C3 can only be <9>
R4C7 can only be <5>
R6C3 can only be <7>
R5C9 can only be <7>
R5C1 can only be <5>
R8C3 can only be <4>
R9C5 can only be <8>
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