Jun 22 - Super Hard
Puzzle Copyright © Kevin Stone
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Reasoning
R2C3 is the only square in row 2 that can be <8>
R3C7 is the only square in row 3 that can be <2>
R3C4 is the only square in row 3 that can be <6>
R3C1 is the only square in row 3 that can be <9>
R7C1 can only be <4>
R4C6 is the only square in row 4 that can be <8>
R6C3 is the only square in row 6 that can be <2>
R6C7 is the only square in row 6 that can be <6>
R7C2 is the only square in column 2 that can be <2>
R1C8 is the only square in column 8 that can be <5>
R1C7 is the only square in row 1 that can be <8>
R1C9 is the only square in row 1 that can be <3>
R9C8 is the only square in row 9 that can be <8>
R5C8 is the only square in column 8 that can be <4>
R4C4 is the only square in row 4 that can be <4>
R1C6 is the only square in row 1 that can be <4>
R2C9 is the only square in row 2 that can be <4>
R8C7 is the only square in row 8 that can be <4>
R4C9 is the only square in column 9 that can be <9>
Squares R3C8 and R3C9 in row 3, R6C1 and R6C8 in row 6 and R8C1 and R8C9 in row 8 form a Swordfish pattern on possibility <7>. All other instances of this possibility in columns 1, 8 and 9 can be removed.
R2C1 - removing <7> from <17> leaving <1>
R9C1 - removing <7> from <357> leaving <35>
R1C4 is the only square in row 1 that can be <1>
R2C4 is the only square in row 2 that can be <7>
Intersection of column 5 with block 5. The value <1> only appears in one or more of squares R4C5, R5C5 and R6C5 of column 5. These squares are the ones that intersect with block 5. Thus, the other (non-intersecting) squares of block 5 cannot contain this value.
R6C6 - removing <1> from <159> leaving <59>
Squares R1C2, R1C3, R9C2 and R9C3 form a Type-3 Unique Rectangle on <67>. Upon close inspection, it is clear that:
(R9C2 or R9C3)<359>, R9C4<359> and R9C1<35> form a naked triplet on <359> in row 9. No other squares in the row can contain these possibilities
R9C6 - removing <59> from <1569> leaving <16>
Squares R2C5, R2C6, R8C5 and R8C6 form a Type-4 Unique Rectangle on <25>.
R8C5 - removing <5> from <235> leaving <23>
R8C6 - removing <5> from <256> leaving <26>
Intersection of block 8 with column 4. The value <5> only appears in one or more of squares R7C4, R8C4 and R9C4 of block 8. These squares are the ones that intersect with column 4. Thus, the other (non-intersecting) squares of column 4 cannot contain this value.
R6C4 - removing <5> from <359> leaving <39>
Squares R9C7 (XY), R9C6 (XZ) and R8C9 (YZ) form an XY-Wing pattern on <6>. All squares that are buddies of both the XZ and YZ squares cannot be <6>.
R8C6 - removing <6> from <26> leaving <2>
R8C5 can only be <3>
R2C6 can only be <5>
R2C5 can only be <2>
R6C6 can only be <9>
R6C4 can only be <3>
R8C4 can only be <5>
R8C1 can only be <7>
R9C4 can only be <9>
R8C9 can only be <6>
R6C1 can only be <5>
R9C2 can only be <6>
R7C9 can only be <1>
R9C6 can only be <1>
R1C2 can only be <7>
R7C3 can only be <9>
R9C7 can only be <7>
R7C6 can only be <6>
R1C3 can only be <6>
R4C2 can only be <1>
R4C5 can only be <5>
R4C7 can only be <3>
R5C2 can only be <9>
R6C5 can only be <1>
R4C3 can only be <7>
R5C7 can only be <1>
R5C3 can only be <3>
R9C3 can only be <5>
R6C8 can only be <7>
R9C1 can only be <3>
R3C8 can only be <1>
R3C9 can only be <7>
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