Sep 23 - Super Hard
Puzzle Copyright © Kevin Stone
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Reasoning
R5C5 can only be <1>
R9C8 can only be <5>
R5C7 can only be <5>
R3C7 can only be <3>
R4C1 is the only square in row 4 that can be <5>
R6C2 is the only square in row 6 that can be <8>
R7C4 is the only square in row 7 that can be <8>
R7C6 is the only square in row 7 that can be <5>
R3C4 is the only square in row 3 that can be <5>
R1C9 is the only square in row 1 that can be <5>
R9C9 is the only square in row 9 that can be <8>
Squares R3C3 and R7C3 in column 3 form a simple naked pair. These 2 squares both contain the 2 possibilities <12>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the column.
R4C3 - removing <12> from <1236> leaving <36>
R5C3 - removing <2> from <24> leaving <4>
R6C3 - removing <1> from <1346> leaving <346>
Squares R4C3 and R6C3 in block 4 form a simple naked pair. These 2 squares both contain the 2 possibilities <36>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the block.
R4C2 - removing <3> from <123> leaving <12>
R6C1 - removing <36> from <1369> leaving <19>
Squares R1C2 and R4C2 in column 2 and R1C8 and R4C8 in column 8 form a Simple X-Wing pattern on possibility <2>. All other instances of this possibility in rows 1 and 4 can be removed.
R1C1 - removing <2> from <1237> leaving <137>
R1C5 - removing <2> from <267> leaving <67>
R1C6 - removing <2> from <1234> leaving <134>
R4C9 - removing <2> from <127> leaving <17>
Squares R4C9 and R8C9 in column 9 form a simple naked pair. These 2 squares both contain the 2 possibilities <17>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the column.
R6C9 - removing <1> from <149> leaving <49>
Squares R3C3 and R7C3 in column 3 and R3C5 and R7C5 in column 5 form a Simple X-Wing pattern on possibility <2>. All other instances of this possibility in rows 3 and 7 can be removed.
R3C6 - removing <2> from <129> leaving <19>
Squares R3C6 (XY), R8C6 (XZ) and R3C5 (YZ) form an XY-Wing pattern on <2>. All squares that are buddies of both the XZ and YZ squares cannot be <2>.
R7C5 - removing <2> from <27> leaving <7>
R2C6 - removing <2> from <234> leaving <34>
R7C7 can only be <1>
R1C5 can only be <6>
R7C3 can only be <2>
R6C7 can only be <6>
R8C9 can only be <7>
R4C9 can only be <1>
R9C5 can only be <9>
R4C2 can only be <2>
R6C3 can only be <3>
R4C7 can only be <7>
R3C3 can only be <1>
R3C5 can only be <2>
R3C6 can only be <9>
R4C8 can only be <3>
R1C2 can only be <3>
R5C1 can only be <9>
R4C3 can only be <6>
R6C8 can only be <4>
R5C9 can only be <2>
R6C1 can only be <1>
R2C9 can only be <4>
R8C1 can only be <6>
R6C9 can only be <9>
R1C8 can only be <2>
R8C4 can only be <1>
R9C1 can only be <3>
R8C6 can only be <2>
R9C6 can only be <4>
R9C2 can only be <1>
R1C1 can only be <7>
R9C4 can only be <6>
R2C6 can only be <3>
R1C4 can only be <4>
R2C1 can only be <2>
R1C6 can only be <1>
R2C4 can only be <7>
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