May 31 - Super Hard
Puzzle Copyright © Kevin Stone
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Reasoning
R7C7 can only be <4>
R8C8 can only be <7>
R9C9 can only be <2>
R1C1 is the only square in row 1 that can be <8>
R1C7 is the only square in row 1 that can be <9>
R2C4 is the only square in row 2 that can be <1>
R2C5 is the only square in row 2 that can be <2>
R2C9 is the only square in row 2 that can be <7>
R4C6 is the only square in row 4 that can be <1>
R7C1 is the only square in row 7 that can be <5>
R7C2 is the only square in row 7 that can be <6>
R8C2 is the only square in row 8 that can be <1>
R8C6 is the only square in row 8 that can be <9>
R6C4 is the only square in row 6 that can be <9>
R5C8 is the only square in row 5 that can be <9>
R8C5 is the only square in row 8 that can be <3>
R6C5 can only be <4>
R4C5 can only be <7>
R5C1 is the only square in row 5 that can be <7>
R6C2 is the only square in column 2 that can be <8>
R3C7 is the only square in column 7 that can be <5>
Squares R1C4 and R1C6 in block 2 form a simple naked pair. These 2 squares both contain the 2 possibilities <34>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the block.
R3C4 - removing <34> from <3467> leaving <67>
R3C6 - removing <34> from <3467> leaving <67>
Squares R3C4 and R3C6 in row 3 form a simple naked pair. These 2 squares both contain the 2 possibilities <67>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the row.
R3C8 - removing <6> from <468> leaving <48>
Squares R8C1 and R8C3 in block 7 form a simple naked pair. These 2 squares both contain the 2 possibilities <24>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the block.
R7C3 - removing <2> from <278> leaving <78>
R9C3 - removing <4> from <478> leaving <78>
Intersection of row 5 with block 5. The value <6> only appears in one or more of squares R5C4, R5C5 and R5C6 of row 5. These squares are the ones that intersect with block 5. Thus, the other (non-intersecting) squares of block 5 cannot contain this value.
R4C4 - removing <6> from <236> leaving <23>
R6C6 - removing <6> from <2356> leaving <235>
R6C1 is the only square in row 6 that can be <6>
Squares R7C3, R9C3, R7C4 and R9C4 form a Type-3 Unique Rectangle on <78>. Upon close inspection, it is clear that:
(R7C4 or R9C4)<24>, R4C4<23> and R1C4<34> form a naked triplet on <234> in column 4. No other squares in the column can contain these possibilities
R5C4 - removing <3> from <36> leaving <6>
(R7C4 or R9C4)<24>, R5C4<36>, R4C4<23> and R1C4<34> form a naked quad on <2346> in column 4. No other squares in the column can contain these possibilities
R3C4 - removing <6> from <67> leaving <7>
R3C6 can only be <6>
Squares R4C1 (XY), R4C4 (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>.
R5C6 - removing <3> from <35> leaving <5>
R6C9 is the only square in row 6 that can be <5>
Squares R3C3 and R5C9 form a remote naked pair. <34> can be removed from any square that is common to their groups.
R3C9 - removing <34> from <348> leaving <8>
R3C8 can only be <4>
R3C3 can only be <3>
R2C8 can only be <6>
R2C7 can only be <3>
R4C8 can only be <8>
R6C3 can only be <2>
R2C2 can only be <4>
R6C6 can only be <3>
R8C3 can only be <4>
R4C1 can only be <4>
R1C6 can only be <4>
R4C4 can only be <2>
R8C1 can only be <2>
R1C4 can only be <3>
R9C6 can only be <7>
R5C2 can only be <3>
R4C7 can only be <6>
R4C9 can only be <3>
R7C4 can only be <8>
R5C9 can only be <4>
R7C3 can only be <7>
R9C4 can only be <4>
R9C3 can only be <8>
R7C6 can only be <2>
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