Jul 17 - Super Hard
Puzzle Copyright © Kevin Stone
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Reasoning
R1C9 can only be <8>
R8C8 is the only square in row 8 that can be <9>
Squares R4C5 and R5C4 in block 5 form a simple naked pair. These 2 squares both contain the 2 possibilities <58>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the block.
R5C5 - removing <58> from <56789> leaving <679>
R6C5 - removing <5> from <569> leaving <69>
Squares R2C7<15>, R2C9<157> and R3C8<17> in block 3 form a comprehensive naked triplet. These 3 squares can only contain the 3 possibilities <157>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the block.
R2C8 - removing <157> from <12457> leaving <24>
Squares R2C3<28>, R2C4<48> and R2C8<24> in row 2 form a comprehensive naked triplet. These 3 squares can only contain the 3 possibilities <248>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the row.
R2C1 - removing <2> from <2679> leaving <679>
R2C2 - removing <28> from <236789> leaving <3679>
R2C5 - removing <48> from <13468> leaving <136>
Squares R5C3 and R8C3 in column 3 and R5C4 and R8C4 in column 4 form a Simple X-Wing pattern on possibility <5>. All other instances of this possibility in rows 5 and 8 can be removed.
R5C2 - removing <5> from <12459> leaving <1249>
R8C2 - removing <5> from <245678> leaving <24678>
R8C5 - removing <5> from <23457> leaving <2347>
R5C7 - removing <5> from <158> leaving <18>
R8C7 - removing <5> from <158> leaving <18>
R5C8 - removing <5> from <13568> leaving <1368>
R5C9 - removing <5> from <135> leaving <13>
R8C9 - removing <5> from <1357> leaving <137>
R2C7 is the only square in column 7 that can be <5>
R9C9 is the only square in column 9 that can be <5>
Squares R3C2 and R3C5 in row 3, R4C5 and R4C8 in row 4 and R9C2 and R9C8 in row 9 form a Swordfish pattern on possibility <8>. All other instances of this possibility in columns 2, 5 and 8 can be removed.
R5C8 - removing <8> from <1368> leaving <136>
R8C2 - removing <8> from <24678> leaving <2467>
Squares R5C3 (XY), R2C3 (XZ) and R5C4 (YZ) form an XY-Wing pattern on <8>. All squares that are buddies of both the XZ and YZ squares cannot be <8>.
R2C4 - removing <8> from <48> leaving <4>
R2C8 can only be <2>
R8C4 can only be <5>
R2C3 can only be <8>
R1C8 can only be <4>
R5C4 can only be <8>
R8C3 can only be <2>
R3C2 can only be <7>
R3C8 can only be <1>
R7C2 can only be <5>
R3C5 can only be <8>
R2C9 can only be <7>
R5C7 can only be <1>
R4C5 can only be <5>
R5C9 can only be <3>
R8C7 can only be <8>
R5C8 can only be <6>
R4C2 can only be <1>
R6C2 can only be <9>
R5C3 can only be <5>
R9C8 can only be <7>
R9C1 can only be <4>
R7C8 can only be <3>
R8C9 can only be <1>
R4C8 can only be <8>
R5C6 can only be <7>
R6C8 can only be <5>
R6C5 can only be <6>
R1C5 can only be <3>
R7C5 can only be <7>
R9C2 can only be <8>
R9C5 can only be <2>
R5C1 can only be <2>
R8C2 can only be <6>
R2C5 can only be <1>
R2C6 can only be <6>
R2C1 can only be <9>
R2C2 can only be <3>
R5C2 can only be <4>
R1C1 can only be <6>
R5C5 can only be <9>
R8C6 can only be <3>
R8C5 can only be <4>
R8C1 can only be <7>
R1C2 can only be <2>
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