May 27 - Super Hard
Puzzle Copyright © Kevin Stone
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Reasoning
R2C6 can only be <8>
R6C2 is the only square in row 6 that can be <3>
R3C2 can only be <6>
R3C1 can only be <8>
R1C9 is the only square in row 1 that can be <8>
R1C3 is the only square in row 1 that can be <3>
R1C1 is the only square in row 1 that can be <2>
R1C7 is the only square in row 1 that can be <1>
R2C7 can only be <5>
R2C8 can only be <2>
R1C4 is the only square in row 1 that can be <4>
R2C4 can only be <6>
R5C8 is the only square in row 5 that can be <8>
R4C4 is the only square in row 4 that can be <8>
R8C7 is the only square in row 8 that can be <6>
R9C3 is the only square in row 9 that can be <2>
R5C2 is the only square in row 5 that can be <2>
R4C6 is the only square in row 4 that can be <2>
R9C1 is the only square in row 9 that can be <6>
R9C9 is the only square in row 9 that can be <4>
R9C6 is the only square in row 9 that can be <3>
R9C5 is the only square in row 9 that can be <5>
R4C2 is the only square in column 2 that can be <9>
R6C6 is the only square in column 6 that can be <5>
R8C4 is the only square in block 8 that can be <1>
Intersection of column 2 with block 7. The value <7> only appears in one or more of squares R7C2, R8C2 and R9C2 of column 2. These squares are the ones that intersect with block 7. Thus, the other (non-intersecting) squares of block 7 cannot contain this value.
R7C1 - removing <7> from <157> leaving <15>
Squares R5C7 and R6C4 form a remote naked pair. <79> can be removed from any square that is common to their groups.
R6C8 - removing <79> from <479> leaving <4>
R6C9 - removing <9> from <169> leaving <16>
R5C5 - removing <79> from <1679> leaving <16>
R4C1 is the only square in row 4 that can be <4>
Intersection of row 4 with block 6. The value <5> only appears in one or more of squares R4C7, R4C8 and R4C9 of row 4. These squares are the ones that intersect with block 6. Thus, the other (non-intersecting) squares of block 6 cannot contain this value.
R5C9 - removing <5> from <1569> leaving <169>
Squares R5C1 and R6C1 in column 1, R6C4 and R9C4 in column 4 and R5C7 and R9C7 in column 7 form a Swordfish pattern on possibility <7>. All other instances of this possibility in rows 5, 6 and 9 can be removed.
R6C5 - removing <7> from <1679> leaving <169>
Squares R7C8 (XYZ), R7C9 (XZ) and R4C8 (YZ) form an XYZ-Wing pattern on <5>. All squares that are buddies of all three squares cannot be <5>.
R8C8 - removing <5> from <579> leaving <79>
R8C3 is the only square in row 8 that can be <5>
R5C3 can only be <1>
R7C1 can only be <1>
R5C5 can only be <6>
R2C3 can only be <4>
R6C1 can only be <7>
R5C9 can only be <9>
R5C7 can only be <7>
R3C9 can only be <3>
R6C4 can only be <9>
R5C1 can only be <5>
R6C5 can only be <1>
R9C4 can only be <7>
R6C9 can only be <6>
R4C5 can only be <7>
R7C2 can only be <7>
R8C2 can only be <4>
R2C2 can only be <1>
R9C7 can only be <9>
R8C6 can only be <9>
R8C8 can only be <7>
R3C8 can only be <9>
R7C9 can only be <5>
R4C8 can only be <5>
R1C5 can only be <9>
R4C9 can only be <1>
R7C8 can only be <3>
R1C6 can only be <7>
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