May 29 - Super Hard
Puzzle Copyright © Kevin Stone
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Reasoning
R3C5 can only be <7>
R3C8 is the only square in row 3 that can be <1>
R3C4 is the only square in row 3 that can be <9>
R4C1 is the only square in row 4 that can be <9>
R6C3 is the only square in row 6 that can be <2>
R8C3 is the only square in row 8 that can be <1>
R9C2 is the only square in row 9 that can be <9>
R7C7 is the only square in row 7 that can be <9>
R7C8 is the only square in row 7 that can be <7>
R9C8 is the only square in column 8 that can be <4>
R3C6 is the only square in block 2 that can be <3>
R3C2 can only be <2>
R1C6 is the only square in column 6 that can be <2>
Squares R1C2<47>, R2C1<347> and R2C3<34> in block 1 form a comprehensive naked triplet. These 3 squares can only contain the 3 possibilities <347>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the block.
R1C1 - removing <47> from <4567> leaving <56>
Squares R2C3<34>, R4C3<48> and R5C3<38> in column 3 form a comprehensive naked triplet. These 3 squares can only contain the 3 possibilities <348>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the column.
R7C3 - removing <34> from <3456> leaving <56>
Squares R1C2 and R7C2 in column 2 and R1C4 and R7C4 in column 4 form a Simple X-Wing pattern on possibility <4>. All other instances of this possibility in rows 1 and 7 can be removed.
R7C5 - removing <4> from <456> leaving <56>
Squares R7C3 and R7C5 in row 7 form a simple naked pair. These 2 squares both contain the 2 possibilities <56>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the row.
R7C4 - removing <6> from <1346> leaving <134>
R7C6 - removing <5> from <15> leaving <1>
Squares R3C3 and R3C7 in row 3, R5C5 and R5C7 in row 5 and R7C3 and R7C5 in row 7 form a Swordfish pattern on possibility <5>. All other instances of this possibility in columns 3, 5 and 7 can be removed.
R4C7 - removing <5> from <4578> leaving <478>
Squares R1C2 (XY), R2C3 (XZ) and R5C2 (YZ) form an XY-Wing pattern on <3>. All squares that are buddies of both the XZ and YZ squares cannot be <3>.
R5C3 - removing <3> from <38> leaving <8>
R5C8 can only be <6>
R4C3 can only be <4>
R5C5 can only be <5>
R1C8 can only be <8>
R1C4 can only be <4>
R2C3 can only be <3>
R6C1 can only be <7>
R5C7 can only be <7>
R7C5 can only be <6>
R5C2 can only be <3>
R2C7 can only be <2>
R4C7 can only be <8>
R6C9 can only be <1>
R6C6 can only be <8>
R6C7 can only be <4>
R4C6 can only be <7>
R9C6 can only be <5>
R4C4 can only be <1>
R6C4 can only be <6>
R4C9 can only be <5>
R7C3 can only be <5>
R8C5 can only be <4>
R2C5 can only be <8>
R7C4 can only be <3>
R1C2 can only be <7>
R2C1 can only be <4>
R2C9 can only be <7>
R8C7 can only be <6>
R1C9 can only be <6>
R7C2 can only be <4>
R3C3 can only be <6>
R9C4 can only be <8>
R8C1 can only be <3>
R3C7 can only be <5>
R9C9 can only be <3>
R9C1 can only be <6>
R8C9 can only be <2>
R1C1 can only be <5>
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