May 16 - Super Hard
Puzzle Copyright © Kevin Stone
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Reasoning
R3C6 can only be <8>
R4C3 can only be <1>
R6C7 can only be <7>
R7C6 can only be <3>
R7C4 can only be <1>
R4C6 can only be <7>
R6C4 can only be <8>
R9C5 can only be <9>
R6C5 can only be <1>
R2C1 is the only square in row 2 that can be <7>
R2C3 is the only square in row 2 that can be <8>
R4C5 is the only square in row 4 that can be <2>
R7C8 is the only square in row 7 that can be <7>
R3C7 is the only square in column 7 that can be <9>
R8C7 is the only square in column 7 that can be <2>
Squares R1C5 and R1C9 in row 1 form a simple naked pair. These 2 squares both contain the 2 possibilities <46>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the row.
R1C2 - removing <46> from <24569> leaving <259>
R1C8 - removing <4> from <245> leaving <25>
Squares R1C1 and R5C1 in column 1 form a simple naked pair. These 2 squares both contain the 2 possibilities <59>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the column.
R8C1 - removing <9> from <389> leaving <38>
Squares R2C8<134>, R8C8<134> and R9C8<13> in column 8 form a comprehensive naked triplet. These 3 squares can only contain the 3 possibilities <134>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the column.
R3C8 - removing <4> from <245> leaving <25>
Squares R8C1, R9C1, R8C9 and R9C9 form a Type-4 Unique Rectangle on <38>.
R8C9 - removing <3> from <1348> leaving <148>
R9C9 - removing <3> from <1368> leaving <168>
Intersection of block 9 with column 8. The value <3> only appears in one or more of squares R7C8, R8C8 and R9C8 of block 9. These squares are the ones that intersect with column 8. Thus, the other (non-intersecting) squares of column 8 cannot contain this value.
R2C8 - removing <3> from <134> leaving <14>
Squares R1C8, R3C8, R1C2 and R3C2 form a Type-3 Unique Rectangle on <25>. Upon close inspection, it is clear that:
(R1C2 or R3C2)<469>, R9C2<16>, R8C2<149> and R2C2<46> form a naked quad on <1469> in column 2. No other squares in the column can contain these possibilities
R7C2 - removing <46> from <456> leaving <5>
Squares R2C2 (XY), R2C8 (XZ) and R9C2 (YZ) form an XY-Wing pattern on <1>. All squares that are buddies of both the XZ and YZ squares cannot be <1>.
R9C8 - removing <1> from <13> leaving <3>
R9C1 can only be <8>
R8C1 can only be <3>
R8C9 is the only square in row 8 that can be <8>
Squares R1C9 (XY), R2C8 (XZ) and R9C9 (YZ) form an XY-Wing pattern on <1>. All squares that are buddies of both the XZ and YZ squares cannot be <1>.
R2C9 - removing <1> from <1346> leaving <346>
R8C8 - removing <1> from <14> leaving <4>
R8C3 can only be <9>
R2C8 can only be <1>
R7C7 can only be <6>
R7C3 can only be <4>
R9C9 can only be <1>
R8C2 can only be <1>
R6C3 can only be <5>
R9C2 can only be <6>
R6C6 can only be <9>
R5C1 can only be <9>
R5C6 can only be <5>
R3C3 can only be <6>
R2C2 can only be <4>
R2C7 can only be <3>
R3C2 can only be <2>
R2C9 can only be <6>
R4C7 can only be <4>
R1C9 can only be <4>
R3C8 can only be <5>
R1C2 can only be <9>
R3C4 can only be <4>
R4C4 can only be <3>
R1C5 can only be <6>
R1C8 can only be <2>
R5C4 can only be <6>
R5C9 can only be <3>
R1C1 can only be <5>
R5C5 can only be <4>
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