Jan 23 - Super Hard
Puzzle Copyright © Kevin Stone
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Reasoning
R5C7 can only be <5>
R6C2 can only be <2>
R6C1 can only be <6>
R5C3 can only be <4>
R5C4 can only be <6>
R4C2 can only be <8>
R2C2 is the only square in column 2 that can be <5>
R3C2 is the only square in column 2 that can be <9>
R9C2 is the only square in column 2 that can be <7>
R5C6 is the only square in column 6 that can be <1>
R5C5 can only be <7>
R6C6 can only be <9>
R6C5 can only be <3>
R6C8 can only be <7>
R3C1 is the only square in row 3 that can be <7>
R2C1 can only be <2>
R8C1 can only be <3>
R8C9 can only be <6>
R9C1 can only be <8>
R2C8 is the only square in row 2 that can be <6>
R7C9 is the only square in row 7 that can be <8>
R9C7 is the only square in row 9 that can be <3>
Squares R1C3 and R3C3 in column 3 form a simple naked pair. These 2 squares both contain the 2 possibilities <18>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the column.
R7C3 - removing <1> from <126> leaving <26>
Intersection of row 2 with block 2. The value <4> only appears in one or more of squares R2C4, R2C5 and R2C6 of row 2. These squares are the ones that intersect with block 2. Thus, the other (non-intersecting) squares of block 2 cannot contain this value.
R3C5 - removing <4> from <248> leaving <28>
Intersection of row 9 with block 8. The values <49> only appears in one or more of squares R9C4, R9C5 and R9C6 of row 9. These squares are the ones that intersect with block 8. Thus, the other (non-intersecting) squares of block 8 cannot contain these values.
R7C5 - removing <49> from <12469> leaving <126>
R8C4 - removing <4> from <245> leaving <25>
R8C5 - removing <4> from <1245> leaving <125>
Squares R4C8, R4C9, R1C8 and R1C9 form a Type-4 Unique Rectangle on <39>.
R1C8 - removing <9> from <1239> leaving <123>
R1C9 - removing <9> from <379> leaving <37>
Squares R7C3, R9C3, R7C5 and R9C5 form a Type-4 Unique Rectangle on <26>.
R7C5 - removing <2> from <126> leaving <16>
R9C5 - removing <2> from <2469> leaving <469>
Squares R1C7 (XY), R1C6 (XZ) and R2C9 (YZ) form an XY-Wing pattern on <7>. All squares that are buddies of both the XZ and YZ squares cannot be <7>.
R2C6 - removing <7> from <47> leaving <4>
R1C9 - removing <7> from <37> leaving <3>
R4C9 can only be <9>
R2C5 can only be <9>
R9C6 can only be <2>
R4C8 can only be <3>
R2C9 can only be <7>
R9C3 can only be <6>
R1C6 can only be <7>
R8C4 can only be <5>
R8C5 can only be <1>
R1C4 can only be <2>
R8C2 can only be <4>
R7C5 can only be <6>
R9C5 can only be <4>
R7C3 can only be <2>
R9C4 can only be <9>
R4C5 can only be <2>
R1C7 can only be <9>
R1C8 can only be <1>
R4C4 can only be <4>
R3C5 can only be <8>
R1C3 can only be <8>
R3C3 can only be <1>
R1C5 can only be <5>
R7C7 can only be <4>
R7C2 can only be <1>
R7C8 can only be <9>
R3C7 can only be <2>
R8C8 can only be <2>
R3C8 can only be <4>
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