Jul 28 - Super Hard
Puzzle Copyright © Kevin Stone
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Reasoning
R4C1 is the only square in row 4 that can be <2>
R4C9 is the only square in row 4 that can be <6>
R6C9 can only be <8>
R5C9 can only be <5>
R5C8 can only be <3>
R5C7 can only be <1>
R6C1 is the only square in row 6 that can be <6>
Squares R2C6<36>, R4C6<38> and R8C6<368> in column 6 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 column.
R3C6 - removing <36> from <13469> leaving <149>
R7C6 - removing <368> from <13689> leaving <19>
Squares R2C4<236>, R2C5<23> and R2C6<36> in row 2 form a comprehensive naked triplet. These 3 squares can only contain the 3 possibilities <236>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the row.
R2C3 - removing <26> from <2678> leaving <78>
R2C7 - removing <23> from <2378> leaving <78>
R3C3 is the only square in column 3 that can be <6>
R3C7 is the only square in column 7 that can be <3>
Intersection of row 2 with block 2. The values <236> only appears in one or more of squares R2C4, R2C5 and R2C6 of row 2. These squares are the ones that intersect with block 2. Thus, the other (non-intersecting) squares of block 2 cannot contain these values.
R1C5 - removing <2> from <125> leaving <15>
R3C4 - removing <2> from <125> leaving <15>
R3C5 - removing <2> from <12459> leaving <1459>
Squares R1C5 and R3C4 in block 2 form a simple naked pair. These 2 squares both contain the 2 possibilities <15>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the block.
R3C5 - removing <15> from <1459> leaving <49>
R3C6 - removing <1> from <149> leaving <49>
Squares R3C1<18>, R3C4<15> and R3C8<58> in row 3 form a comprehensive naked triplet. These 3 squares can only contain the 3 possibilities <158>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the row.
R3C2 - removing <8> from <278> leaving <27>
Squares R1C3 and R1C5 in row 1 and R9C3 and R9C5 in row 9 form a Simple X-Wing pattern on possibility <1>. All other instances of this possibility in columns 3 and 5 can be removed.
R6C5 - removing <1> from <147> leaving <47>
R7C3 - removing <1> from <12348> leaving <2348>
R7C5 - removing <1> from <123789> leaving <23789>
Squares R3C2 and R7C2 in column 2 and R3C9 and R7C9 in column 9 form a Simple X-Wing pattern on possibility <2>. All other instances of this possibility in rows 3 and 7 can be removed.
R7C3 - removing <2> from <2348> leaving <348>
R7C4 - removing <2> from <12367> leaving <1367>
R7C5 - removing <2> from <23789> leaving <3789>
R7C7 - removing <2> from <25678> leaving <5678>
Squares R3C1, R5C1 and R7C1 in column 1, R5C2 and R7C2 in column 2 and R3C8 and R7C8 in column 8 form a Swordfish pattern on possibility <8>. All other instances of this possibility in rows 3, 5 and 7 can be removed.
R5C3 - removing <8> from <478> leaving <47>
R7C3 - removing <8> from <348> leaving <34>
R7C5 - removing <8> from <3789> leaving <379>
R7C7 - removing <8> from <5678> leaving <567>
Squares R1C7 (XY), R9C7 (XZ) and R3C8 (YZ) form an XY-Wing pattern on <8>. All squares that are buddies of both the XZ and YZ squares cannot be <8>.
R7C8 - removing <8> from <58> leaving <5>
R2C7 - removing <8> from <78> leaving <7>
R2C3 can only be <8>
R3C9 can only be <2>
R3C2 can only be <7>
R7C9 can only be <7>
R1C7 can only be <5>
R7C7 can only be <6>
R3C8 can only be <8>
R1C5 can only be <1>
R3C1 can only be <1>
R3C4 can only be <5>
R1C3 can only be <2>
R5C2 can only be <8>
R4C4 can only be <3>
R4C6 can only be <8>
R4C5 can only be <5>
R5C1 can only be <4>
R7C2 can only be <2>
R8C3 can only be <3>
R9C3 can only be <1>
R7C4 can only be <1>
R8C6 can only be <6>
R7C3 can only be <4>
R2C6 can only be <3>
R2C5 can only be <2>
R5C3 can only be <7>
R7C1 can only be <8>
R7C6 can only be <9>
R6C4 can only be <7>
R7C5 can only be <3>
R3C6 can only be <4>
R2C4 can only be <6>
R9C5 can only be <8>
R3C5 can only be <9>
R6C6 can only be <1>
R6C5 can only be <4>
R8C4 can only be <2>
R8C7 can only be <8>
R8C5 can only be <7>
R9C7 can only be <2>
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