Jun 16 - Super Hard
Puzzle Copyright © Kevin Stone
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Reasoning
R3C4 is the only square in row 3 that can be <4>
R3C1 is the only square in row 3 that can be <1>
R5C8 is the only square in row 5 that can be <4>
R6C5 is the only square in row 6 that can be <2>
R7C9 is the only square in row 7 that can be <6>
R2C8 is the only square in row 2 that can be <6>
R7C1 is the only square in row 7 that can be <4>
R8C2 is the only square in row 8 that can be <2>
R2C9 is the only square in row 2 that can be <2>
R1C3 is the only square in row 1 that can be <2>
R9C1 is the only square in row 9 that can be <9>
R8C8 is the only square in column 8 that can be <7>
R1C7 is the only square in column 7 that can be <7>
R1C9 is the only square in column 9 that can be <9>
Intersection of row 5 with block 4. The value <5> only appears in one or more of squares R5C1, R5C2 and R5C3 of row 5. These squares are the ones that intersect with block 4. Thus, the other (non-intersecting) squares of block 4 cannot contain this value.
R4C1 - removing <5> from <35678> leaving <3678>
R4C3 - removing <5> from <357> leaving <37>
Intersection of column 3 with block 4. The value <3> only appears in one or more of squares R4C3, R5C3 and R6C3 of column 3. These squares are the ones that intersect with block 4. Thus, the other (non-intersecting) squares of block 4 cannot contain this value.
R4C1 - removing <3> from <3678> leaving <678>
R6C1 - removing <3> from <3678> leaving <678>
Squares R4C3 and R9C3 in column 3 and R4C4 and R9C4 in column 4 form a Simple X-Wing pattern on possibility <7>. All other instances of this possibility in rows 4 and 9 can be removed.
R4C1 - removing <7> from <678> leaving <68>
Squares R3C8, R3C9, R4C8 and R4C9 form a Type-1 Unique Rectangle on <58>.
R4C9 - removing <58> from <1358> leaving <13>
R4C8 is the only square in row 4 that can be <5>
R3C8 can only be <8>
R3C9 can only be <5>
Squares R7C2 (XY), R2C2 (XZ) and R8C1 (YZ) form an XY-Wing pattern on <5>. All squares that are buddies of both the XZ and YZ squares cannot be <5>.
R1C1 - removing <5> from <35> leaving <3>
R2C1 - removing <5> from <357> leaving <37>
R2C1 can only be <7>
R2C2 can only be <5>
R5C3 is the only square in row 5 that can be <5>
R9C3 can only be <7>
R4C3 can only be <3>
R7C2 can only be <8>
R4C9 can only be <1>
R7C6 can only be <7>
R5C2 can only be <1>
R8C1 can only be <5>
R6C2 can only be <7>
R4C4 is the only square in row 4 that can be <7>
R6C6 is the only square in row 6 that can be <1>
R6C9 is the only square in row 6 that can be <3>
R9C5 is the only square in row 9 that can be <5>
R1C5 can only be <8>
R1C6 can only be <5>
R4C5 can only be <6>
R4C1 can only be <8>
R5C5 can only be <3>
R2C5 can only be <1>
R8C5 can only be <4>
R6C1 can only be <6>
R6C7 can only be <8>
R5C7 can only be <6>
R9C7 can only be <1>
R8C9 can only be <8>
R8C6 can only be <3>
R9C9 can only be <4>
R9C4 can only be <8>
R8C4 can only be <1>
R2C6 can only be <9>
R5C4 can only be <9>
R2C4 can only be <3>
R5C6 can only be <8>
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