Jul 11 - Super Hard
Puzzle Copyright © Kevin Stone
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Reasoning
R1C9 can only be <1>
R4C2 can only be <6>
R3C7 can only be <9>
R6C2 can only be <2>
R5C1 can only be <3>
R5C2 can only be <4>
R1C1 can only be <9>
R5C5 is the only square in row 5 that can be <2>
R8C8 is the only square in row 8 that can be <3>
R8C2 is the only square in row 8 that can be <9>
R2C4 is the only square in column 4 that can be <9>
R6C5 is the only square in column 5 that can be <6>
R6C8 can only be <9>
R4C8 can only be <1>
R4C5 can only be <9>
Intersection of row 3 with block 1. The value <1> only appears in one or more of squares R3C1, R3C2 and R3C3 of row 3. These squares are the ones that intersect with block 1. Thus, the other (non-intersecting) squares of block 1 cannot contain this value.
R2C2 - removing <1> from <13578> leaving <3578>
R2C3 - removing <1> from <147> leaving <47>
Intersection of block 8 with row 8. The values <47> only appears in one or more of squares R8C4, R8C5 and R8C6 of block 8. These squares are the ones that intersect with row 8. Thus, the other (non-intersecting) squares of row 8 cannot contain these values.
R8C3 - removing <7> from <167> leaving <16>
R8C7 - removing <7> from <167> leaving <16>
Squares R8C3 and R8C7 in row 8 form a simple naked pair. These 2 squares both contain the 2 possibilities <16>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the row.
R8C4 - removing <1> from <17> leaving <7>
R8C5 - removing <1> from <145> leaving <45>
R8C6 - removing <1> from <147> leaving <47>
R8C9 - removing <6> from <2568> leaving <258>
R8C6 can only be <4>
R5C4 can only be <1>
R8C5 can only be <5>
R2C6 can only be <1>
R5C6 can only be <7>
R9C5 can only be <1>
Squares R3C2 and R3C8 in row 3 and R7C2 and R7C8 in row 7 form a Simple X-Wing pattern on possibility <5>. All other instances of this possibility in columns 2 and 8 can be removed.
R2C2 - removing <5> from <3578> leaving <378>
R2C8 - removing <5> from <24567> leaving <2467>
R9C2 - removing <5> from <578> leaving <78>
R9C8 - removing <5> from <2578> leaving <278>
Squares R1C2<37>, R2C2<378> and R9C2<78> in column 2 form a comprehensive naked triplet. These 3 squares can only contain the 3 possibilities <378>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the column.
R7C2 - removing <7> from <157> leaving <15>
Squares R1C2 and R1C8 in row 1 and R9C2 and R9C8 in row 9 form a Simple X-Wing pattern on possibility <7>. All other instances of this possibility in columns 2 and 8 can be removed.
R2C2 - removing <7> from <378> leaving <38>
R2C8 - removing <7> from <2467> leaving <246>
R7C8 - removing <7> from <567> leaving <56>
Squares R1C2 (XY), R1C5 (XZ) and R2C3 (YZ) form an XY-Wing pattern on <4>. All squares that are buddies of both the XZ and YZ squares cannot be <4>.
R2C5 - removing <4> from <34> leaving <3>
R2C2 can only be <8>
R1C5 can only be <4>
R1C8 can only be <7>
R1C2 can only be <3>
R2C7 can only be <6>
R2C1 can only be <5>
R9C2 can only be <7>
R8C7 can only be <1>
R8C3 can only be <6>
R7C7 can only be <7>
R2C9 can only be <2>
R3C2 can only be <1>
R2C8 can only be <4>
R8C9 can only be <8>
R3C3 can only be <4>
R7C2 can only be <5>
R3C8 can only be <5>
R2C3 can only be <7>
R7C8 can only be <6>
R7C3 can only be <1>
R5C8 can only be <8>
R8C1 can only be <2>
R5C9 can only be <6>
R9C9 can only be <5>
R9C8 can only be <2>
R9C1 can only be <8>
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