Sep 16 - Super Hard
Puzzle Copyright © Kevin Stone
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Reasoning
R1C2 is the only square in row 1 that can be <7>
R1C7 is the only square in row 1 that can be <8>
R5C5 is the only square in row 5 that can be <7>
R4C1 is the only square in row 4 that can be <7>
R3C3 is the only square in column 3 that can be <2>
R7C3 is the only square in column 3 that can be <4>
R7C7 can only be <2>
R9C7 is the only square in column 7 that can be <3>
R8C2 is the only square in row 8 that can be <3>
R2C5 is the only square in row 2 that can be <3>
R1C3 is the only square in row 1 that can be <3>
Intersection of row 4 with block 5. The values <18> only appears in one or more of squares R4C4, R4C5 and R4C6 of row 4. These squares are the ones that intersect with block 5. Thus, the other (non-intersecting) squares of block 5 cannot contain these values.
R5C4 - removing <1> from <1259> leaving <259>
R5C6 - removing <1> from <1456> leaving <456>
Squares R2C1<158>, R3C1<15> and R8C1<18> in column 1 form a comprehensive naked triplet. These 3 squares can only contain the 3 possibilities <158>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the column.
R7C1 - removing <1> from <169> leaving <69>
Squares R6C1<69>, R6C4<59> and R6C5<569> in row 6 form a comprehensive naked triplet. These 3 squares can only contain the 3 possibilities <569>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the row.
R6C6 - removing <56> from <3456> leaving <34>
R6C9 - removing <5> from <345> leaving <34>
Intersection of row 6 with block 5. The value <5> only appears in one or more of squares R6C4, R6C5 and R6C6 of row 6. These squares are the ones that intersect with block 5. Thus, the other (non-intersecting) squares of block 5 cannot contain this value.
R5C4 - removing <5> from <259> leaving <29>
R5C6 - removing <5> from <456> leaving <46>
Squares R5C3 and R5C4 in row 5 and R9C3 and R9C4 in row 9 form a Simple X-Wing pattern on possibility <9>. All other instances of this possibility in columns 3 and 4 can be removed.
R6C4 - removing <9> from <59> leaving <5>
R1C4 can only be <1>
Squares R1C6 and R1C8 in row 1 and R9C6 and R9C8 in row 9 form a Simple X-Wing pattern on possibility <5>. All other instances of this possibility in columns 6 and 8 can be removed.
R2C8 - removing <5> from <125> leaving <12>
R5C8 - removing <5> from <245> leaving <24>
R8C8 - removing <5> from <145> leaving <14>
R5C7 is the only square in row 5 that can be <5>
R3C7 can only be <4>
Squares R2C8<12>, R5C8<24> and R8C8<14> in column 8 form a comprehensive naked triplet. These 3 squares can only contain the 3 possibilities <124>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the column.
R9C8 - removing <1> from <156> leaving <56>
Squares R7C5 (XY), R4C5 (XZ) and R9C4 (YZ) form an XY-Wing pattern on <8>. All squares that are buddies of both the XZ and YZ squares cannot be <8>.
R4C4 - removing <8> from <28> leaving <2>
R8C5 - removing <8> from <158> leaving <15>
R4C9 can only be <3>
R5C4 can only be <9>
R4C6 can only be <1>
R6C9 can only be <4>
R5C3 can only be <1>
R9C4 can only be <8>
R6C5 can only be <6>
R6C1 can only be <9>
R3C5 can only be <5>
R5C6 can only be <4>
R6C6 can only be <3>
R5C8 can only be <2>
R3C1 can only be <1>
R8C5 can only be <1>
R1C6 can only be <6>
R4C5 can only be <8>
R9C6 can only be <5>
R5C2 can only be <6>
R9C3 can only be <9>
R2C8 can only be <1>
R7C1 can only be <6>
R7C9 can only be <1>
R9C2 can only be <1>
R7C5 can only be <9>
R3C9 can only be <6>
R8C9 can only be <5>
R8C8 can only be <4>
R8C1 can only be <8>
R2C9 can only be <2>
R9C8 can only be <6>
R2C2 can only be <8>
R1C8 can only be <5>
R2C1 can only be <5>
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