Aug 19 - Super Hard
Puzzle Copyright © Kevin Stone
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Reasoning
R8C5 can only be <2>
R5C5 can only be <7>
R5C2 can only be <5>
R5C8 can only be <8>
R4C9 can only be <7>
R6C9 can only be <2>
R5C4 can only be <2>
R4C1 can only be <1>
R5C6 can only be <9>
R6C4 can only be <1>
R6C1 can only be <7>
R6C5 can only be <6>
R6C6 can only be <3>
R1C4 can only be <4>
R9C4 can only be <8>
R4C5 can only be <4>
R4C6 can only be <8>
R9C6 can only be <1>
R1C6 can only be <2>
R4C4 can only be <5>
R2C5 can only be <1>
R1C7 is the only square in row 1 that can be <1>
Squares R8C2 and R8C8 in row 8 form a simple naked pair. These 2 squares both contain the 2 possibilities <79>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the row.
R8C1 - removing <9> from <589> leaving <58>
R8C9 - removing <9> from <589> leaving <58>
Squares R7C7<28>, R8C9<58> and R9C7<25> in block 9 form a comprehensive naked triplet. These 3 squares can only contain the 3 possibilities <258>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the block.
R7C9 - removing <8> from <489> leaving <49>
R9C9 - removing <5> from <345> leaving <34>
Squares R3C3 and R3C9 in row 3 and R7C3 and R7C9 in row 7 form a Simple X-Wing pattern on possibility <4>. All other instances of this possibility in columns 3 and 9 can be removed.
R2C9 - removing <4> from <3468> leaving <368>
R9C3 - removing <4> from <457> leaving <57>
R9C9 - removing <4> from <34> leaving <3>
Squares R1C3 and R9C3 in column 3 form a simple naked pair. These 2 squares both contain the 2 possibilities <57>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the column.
R3C3 - removing <5> from <458> leaving <48>
Squares R2C1 and R2C9 in row 2 and R8C1 and R8C9 in row 8 form a Simple X-Wing pattern on possibility <8>. All other instances of this possibility in columns 1 and 9 can be removed.
R3C1 - removing <8> from <589> leaving <59>
R3C9 - removing <8> from <4589> leaving <459>
R7C1 - removing <8> from <289> leaving <29>
Squares R3C1 and R3C9 in row 3 and R7C1 and R7C9 in row 7 form a Simple X-Wing pattern on possibility <9>. All other instances of this possibility in columns 1 and 9 can be removed.
R1C1 - removing <9> from <3569> leaving <356>
R1C9 - removing <9> from <569> leaving <56>
Squares R1C9<56>, R2C9<68> and R3C7<58> in block 3 form a comprehensive naked triplet. These 3 squares can only contain the 3 possibilities <568>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the block.
R3C9 - removing <5> from <459> leaving <49>
Squares R2C2 (XY), R3C3 (XZ) and R2C9 (YZ) form an XY-Wing pattern on <8>. All squares that are buddies of both the XZ and YZ squares cannot be <8>.
R2C1 - removing <8> from <368> leaving <36>
R3C7 - removing <8> from <58> leaving <5>
R3C1 can only be <9>
R9C7 can only be <2>
R1C9 can only be <6>
R7C7 can only be <8>
R2C9 can only be <8>
R8C9 can only be <5>
R3C9 can only be <4>
R7C1 can only be <2>
R1C2 can only be <7>
R3C3 can only be <8>
R7C9 can only be <9>
R2C8 can only be <3>
R7C3 can only be <4>
R8C8 can only be <7>
R8C2 can only be <9>
R9C8 can only be <4>
R8C1 can only be <8>
R1C3 can only be <5>
R9C2 can only be <6>
R1C1 can only be <3>
R9C3 can only be <7>
R2C1 can only be <6>
R1C8 can only be <9>
R9C1 can only be <5>
R2C2 can only be <4>
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