May 26 - Super Hard
Puzzle Copyright © Kevin Stone
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Reasoning
R1C4 can only be <5>
R3C4 can only be <2>
R2C4 can only be <3>
R2C5 can only be <6>
R3C5 can only be <1>
R2C8 is the only square in row 2 that can be <2>
R4C3 is the only square in row 4 that can be <6>
R4C5 is the only square in row 4 that can be <7>
R6C7 is the only square in row 6 that can be <8>
R7C2 is the only square in row 7 that can be <1>
R9C6 is the only square in row 9 that can be <9>
R4C6 is the only square in column 6 that can be <1>
R4C9 can only be <9>
R4C4 can only be <4>
R4C8 can only be <3>
R6C4 can only be <9>
Intersection of row 6 with block 4. The value <4> only appears in one or more of squares R6C1, R6C2 and R6C3 of row 6. These squares are the ones that intersect with block 4. Thus, the other (non-intersecting) squares of block 4 cannot contain this value.
R5C1 - removing <4> from <347> leaving <37>
R5C2 - removing <4> from <2479> leaving <279>
R5C3 - removing <4> from <249> leaving <29>
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.
R5C5 - removing <5> from <235> leaving <23>
Squares R1C2<46>, R1C3<48> and R3C1<68> in block 1 form a comprehensive naked triplet. These 3 squares can only contain the 3 possibilities <468>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the block.
R3C3 - removing <8> from <589> leaving <59>
Squares R1C2 and R1C8 in row 1 and R8C2 and R8C8 in row 8 form a Simple X-Wing pattern on possibility <6>. All other instances of this possibility in columns 2 and 8 can be removed.
R3C8 - removing <6> from <568> leaving <58>
R9C2 - removing <6> from <4567> leaving <457>
R9C8 - removing <6> from <456> leaving <45>
Squares R1C9 (XY), R5C9 (XZ) and R3C8 (YZ) form an XY-Wing pattern on <5>. All squares that are buddies of both the XZ and YZ squares cannot be <5>.
R3C9 - removing <5> from <578> leaving <78>
R5C8 - removing <5> from <145> leaving <14>
Squares R5C8 (XY), R5C9 (XZ) and R9C8 (YZ) form an XY-Wing pattern on <5>. All squares that are buddies of both the XZ and YZ squares cannot be <5>.
R7C9 - removing <5> from <578> leaving <78>
R5C9 is the only square in column 9 that can be <5>
R5C7 can only be <4>
R5C8 can only be <1>
R1C9 is the only square in row 1 that can be <1>
Squares R1C3 and R1C8 in row 1 and R8C3 and R8C8 in row 8 form a Simple X-Wing pattern on possibility <8>. All other instances of this possibility in columns 3 and 8 can be removed.
R3C8 - removing <8> from <58> leaving <5>
R7C3 - removing <8> from <2458> leaving <245>
R3C3 can only be <9>
R9C8 can only be <4>
R2C7 can only be <9>
R2C2 can only be <5>
R5C3 can only be <2>
R5C5 can only be <3>
R6C2 can only be <4>
R5C1 can only be <7>
R6C1 can only be <3>
R1C2 can only be <6>
R1C8 can only be <8>
R3C1 can only be <8>
R1C3 can only be <4>
R8C8 can only be <6>
R3C9 can only be <7>
R8C2 can only be <2>
R9C2 can only be <7>
R3C7 can only be <6>
R7C9 can only be <8>
R5C2 can only be <9>
R7C1 can only be <4>
R9C1 can only be <6>
R7C3 can only be <5>
R7C5 can only be <2>
R7C7 can only be <7>
R8C3 can only be <8>
R7C6 can only be <3>
R6C5 can only be <5>
R8C6 can only be <5>
R8C5 can only be <4>
R6C6 can only be <2>
R9C7 can only be <5>
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