Sep 12 - Super Hard
Puzzle Copyright © Kevin Stone
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Reasoning
R4C5 can only be <3>
R6C1 can only be <8>
R4C9 can only be <7>
R5C5 can only be <4>
R6C5 can only be <9>
R4C2 can only be <1>
R6C3 can only be <7>
R2C1 can only be <6>
R4C3 can only be <2>
R4C7 can only be <6>
R3C2 can only be <9>
R5C2 can only be <3>
R5C8 can only be <1>
R1C2 can only be <8>
R7C2 can only be <7>
R8C2 can only be <6>
R1C5 is the only square in row 1 that can be <6>
R2C4 is the only square in row 2 that can be <4>
R3C8 is the only square in row 3 that can be <6>
Squares R8C6 and R8C9 in row 8 form a simple naked pair. These 2 squares both contain the 2 possibilities <39>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the row.
R8C3 - removing <9> from <189> leaving <18>
Squares R1C3 and R3C3 in column 3 form a simple naked pair. These 2 squares both contain the 2 possibilities <15>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the column.
R8C3 - removing <1> from <18> leaving <8>
R9C3 - removing <1> from <1489> leaving <489>
Squares R7C3 and R7C6 in row 7 form a simple naked pair. These 2 squares both contain the 2 possibilities <49>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the row.
R7C8 - removing <9> from <589> leaving <58>
Intersection of row 2 with block 3. The values <89> only appears in one or more of squares R2C7, R2C8 and R2C9 of row 2. These squares are the ones that intersect with block 3. Thus, the other (non-intersecting) squares of block 3 cannot contain these values.
R1C9 - removing <9> from <359> leaving <35>
Intersection of column 9 with block 3. The value <5> only appears in one or more of squares R1C9, R2C9 and R3C9 of column 9. These squares are the ones that intersect with block 3. Thus, the other (non-intersecting) squares of block 3 cannot contain this value.
R1C7 - removing <5> from <1357> leaving <137>
R2C7 - removing <5> from <578> leaving <78>
R2C8 - removing <5> from <589> leaving <89>
R3C7 - removing <5> from <135> leaving <13>
Squares R7C3, R7C6, R9C3 and R9C6 form a Type-1 Unique Rectangle on <49>.
R9C6 - removing <49> from <3479> leaving <37>
R9C3 is the only square in row 9 that can be <4>
R7C3 can only be <9>
R7C6 can only be <4>
Squares R8C1, R8C5, R9C1 and R9C5 form a Type-1 Unique Rectangle on <12>.
R9C5 - removing <12> from <1278> leaving <78>
R9C1 is the only square in row 9 that can be <1>
R8C1 can only be <2>
R8C5 can only be <1>
Squares R1C9 (XY), R3C7 (XZ) and R1C3 (YZ) form an XY-Wing pattern on <1>. All squares that are buddies of both the XZ and YZ squares cannot be <1>.
R1C7 - removing <1> from <137> leaving <37>
R3C3 - removing <1> from <15> leaving <5>
R3C5 can only be <2>
R1C3 can only be <1>
R3C4 can only be <3>
R7C5 can only be <8>
R7C8 can only be <5>
R9C5 can only be <7>
R7C7 can only be <2>
R6C8 can only be <3>
R9C6 can only be <3>
R2C5 can only be <5>
R8C6 can only be <9>
R2C9 can only be <9>
R2C8 can only be <8>
R8C9 can only be <3>
R3C7 can only be <1>
R1C4 can only be <9>
R6C7 can only be <5>
R9C7 can only be <8>
R1C6 can only be <7>
R9C4 can only be <2>
R1C9 can only be <5>
R9C8 can only be <9>
R2C7 can only be <7>
R1C7 can only be <3>
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