Jul 27 - Super Hard
Puzzle Copyright © Kevin Stone
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Reasoning
R4C6 can only be <9>
R5C3 can only be <3>
R4C4 can only be <3>
R2C6 can only be <2>
R5C2 can only be <7>
R4C2 can only be <8>
R2C4 can only be <9>
R6C6 can only be <7>
R8C6 can only be <1>
R4C8 can only be <4>
R6C4 can only be <2>
R6C2 can only be <6>
R6C8 can only be <3>
R5C5 can only be <1>
R8C4 can only be <5>
Squares R1C9 and R9C9 in column 9 form a simple naked pair. These 2 squares both contain the 2 possibilities <49>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the column.
R2C9 - removing <4> from <346> leaving <36>
R8C9 - removing <49> from <3469> leaving <36>
Squares R5C8<29>, R7C8<259> and R9C8<259> in column 8 form a comprehensive naked triplet. These 3 squares can only contain the 3 possibilities <259>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the column.
R1C8 - removing <9> from <89> leaving <8>
R3C8 - removing <9> from <1689> leaving <168>
R8C8 - removing <29> from <2679> leaving <67>
R1C1 can only be <2>
R9C1 can only be <5>
R2C2 is the only square in row 2 that can be <5>
R7C8 is the only square in row 7 that can be <5>
Squares R3C7<39>, R5C7<29> and R7C7<239> in column 7 form a comprehensive naked triplet. These 3 squares can only contain the 3 possibilities <239>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the column.
R2C7 - removing <3> from <347> leaving <47>
R8C7 - removing <239> from <23479> leaving <47>
Squares R2C1<38>, R2C5<68> and R2C9<36> in row 2 form a comprehensive naked triplet. These 3 squares can only contain the 3 possibilities <368>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the row.
R2C3 - removing <8> from <148> leaving <14>
R2C8 - removing <6> from <167> leaving <17>
Squares R3C2 and R3C7 in row 3 and R7C2 and R7C7 in row 7 form a Simple X-Wing pattern on possibility <3>. All other instances of this possibility in columns 2 and 7 can be removed.
R8C2 - removing <3> from <2349> leaving <249>
Squares R1C2<49>, R8C2<249> and R9C2<249> in column 2 form a comprehensive naked triplet. These 3 squares can only contain the 3 possibilities <249>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the column.
R3C2 - removing <9> from <139> leaving <13>
R7C2 - removing <29> from <1239> leaving <13>
Squares R1C2 and R1C9 in row 1 and R9C2 and R9C9 in row 9 form a Simple X-Wing pattern on possibility <4>. All other instances of this possibility in columns 2 and 9 can be removed.
R8C2 - removing <4> from <249> leaving <29>
Squares R8C2 and R8C5 in row 8 form a simple naked pair. These 2 squares both contain the 2 possibilities <29>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the row.
R8C3 - removing <9> from <489> leaving <48>
Squares R2C3 (XY), R7C3 (XZ) and R1C2 (YZ) form an XY-Wing pattern on <9>. All squares that are buddies of both the XZ and YZ squares cannot be <9>.
R8C2 - removing <9> from <29> leaving <2>
R9C2 - removing <9> from <249> leaving <24>
R3C3 - removing <9> from <189> leaving <18>
R8C5 can only be <9>
R9C2 can only be <4>
R7C5 can only be <2>
R9C9 can only be <9>
R1C2 can only be <9>
R8C3 can only be <8>
R9C8 can only be <2>
R1C9 can only be <4>
R2C7 can only be <7>
R2C8 can only be <1>
R8C7 can only be <4>
R2C3 can only be <4>
R3C8 can only be <6>
R3C5 can only be <8>
R8C8 can only be <7>
R2C9 can only be <3>
R7C7 can only be <3>
R7C2 can only be <1>
R3C7 can only be <9>
R8C9 can only be <6>
R8C1 can only be <3>
R3C3 can only be <1>
R5C8 can only be <9>
R2C1 can only be <8>
R3C2 can only be <3>
R7C3 can only be <9>
R2C5 can only be <6>
R5C7 can only be <2>
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