May 23 - Super Hard
Puzzle Copyright © Kevin Stone
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Reasoning
R1C5 is the only square in row 1 that can be <2>
R5C4 is the only square in row 5 that can be <4>
R7C9 is the only square in row 7 that can be <8>
R3C1 is the only square in row 3 that can be <8>
R1C7 is the only square in row 1 that can be <8>
R1C9 is the only square in row 1 that can be <4>
R5C5 is the only square in row 5 that can be <8>
R4C3 is the only square in row 4 that can be <8>
R4C5 is the only square in row 4 that can be <5>
R8C2 is the only square in row 8 that can be <2>
R9C7 is the only square in row 9 that can be <4>
R6C3 is the only square in block 4 that can be <3>
Squares R5C1 and R5C2 in row 5 form a simple naked pair. These 2 squares both contain the 2 possibilities <59>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the row.
R5C8 - removing <9> from <1679> leaving <167>
Squares R1C1 and R1C3 in block 1 form a simple naked pair. These 2 squares both contain the 2 possibilities <79>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the block.
R2C3 - removing <7> from <57> leaving <5>
R3C8 is the only square in row 3 that can be <5>
R8C7 is the only square in row 8 that can be <5>
Squares R2C2 and R3C2 in column 2 form a simple naked pair. These 2 squares both contain the 2 possibilities <36>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the column.
R7C2 - removing <3> from <359> leaving <59>
Intersection of row 6 with block 5. The values <27> 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 these values.
R5C6 - removing <7> from <167> leaving <16>
Squares R5C1, R5C2, R7C1 and R7C2 form a Type-1 Unique Rectangle on <59>.
R7C1 - removing <59> from <359> leaving <3>
R9C1 can only be <7>
R9C3 can only be <1>
R1C1 can only be <9>
R9C9 can only be <6>
R8C3 can only be <9>
R9C5 can only be <3>
R1C3 can only be <7>
R5C1 can only be <5>
R5C2 can only be <9>
R7C2 can only be <5>
R8C8 can only be <1>
R8C5 can only be <6>
R7C8 can only be <9>
R2C2 is the only square in row 2 that can be <3>
R3C2 can only be <6>
Squares R2C5 and R6C5 in column 5 and R2C7 and R6C7 in column 7 form a Simple X-Wing pattern on possibility <1>. All other instances of this possibility in rows 2 and 6 can be removed.
R6C4 - removing <1> from <129> leaving <29>
R6C6 - removing <1> from <127> leaving <27>
Squares R6C6 (XY), R7C6 (XZ) and R6C5 (YZ) form an XY-Wing pattern on <1>. All squares that are buddies of both the XZ and YZ squares cannot be <1>.
R5C6 - removing <1> from <16> leaving <6>
R5C8 can only be <7>
R4C6 can only be <3>
R5C9 can only be <1>
R2C8 can only be <6>
R3C9 can only be <7>
R6C7 can only be <9>
R6C4 can only be <2>
R4C7 can only be <6>
R2C7 can only be <1>
R4C4 can only be <9>
R3C6 can only be <1>
R6C6 can only be <7>
R7C4 can only be <1>
R6C5 can only be <1>
R7C6 can only be <2>
R3C4 can only be <3>
R2C5 can only be <7>
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