The full reasoning can be found below the Sudoku.
Mar 30 - Very Hard
Puzzle Copyright © Kevin Stone
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Reasoning
R2C5 can only be <7>
R2C9 can only be <5>
R3C4 can only be <5>
R3C6 can only be <8>
R2C1 can only be <9>
R1C9 is the only square in row 1 that can be <1>
R1C4 is the only square in row 1 that can be <9>
R6C7 is the only square in row 6 that can be <5>
R6C3 is the only square in row 6 that can be <9>
R9C9 is the only square in row 9 that can be <9>
Squares R1C5 and R8C5 in column 5 form a simple naked pair. These 2 squares both contain the 2 possibilities <36>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the column.
R5C5 - removing <3> from <234> leaving <24>
R9C5 - removing <36> from <2346> leaving <24>
Intersection of row 5 with block 4. The value <1> only appears in one or more of squares R5C1, R5C2 and R5C3 of row 5. These squares are the ones that intersect with block 4. Thus, the other (non-intersecting) squares of block 4 cannot contain this value.
R6C1 - removing <1> from <1246> leaving <246>
Intersection of row 5 with block 6. The value <3> only appears in one or more of squares R5C7, R5C8 and R5C9 of row 5. These squares are the ones that intersect with block 6. Thus, the other (non-intersecting) squares of block 6 cannot contain this value.
R4C9 - removing <3> from <23468> leaving <2468>
Intersection of column 9 with block 6. The values <68> only appears in one or more of squares R4C9, R5C9 and R6C9 of column 9. These squares are the ones that intersect with block 6. Thus, the other (non-intersecting) squares of block 6 cannot contain these values.
R4C7 - removing <8> from <248> leaving <24>
R5C8 - removing <8> from <238> leaving <23>
Squares R5C5<24>, R6C4<12> and R6C6<14> in block 5 form a comprehensive naked triplet. These 3 squares can only contain the 3 possibilities <124>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the block.
R4C4 - removing <2> from <237> leaving <37>
R4C6 - removing <4> from <347> leaving <37>
Squares R1C3 and R4C3 in column 3 and R1C7 and R4C7 in column 7 form a Simple X-Wing pattern on possibility <4>. All other instances of this possibility in rows 1 and 4 can be removed.
R1C1 - removing <4> from <2457> leaving <257>
R4C1 - removing <4> from <2468> leaving <268>
R4C9 - removing <4> from <2468> leaving <268>
Squares R3C1 and R3C9 in row 3, R6C1, R6C4 and R6C9 in row 6 and R7C4 and R7C9 in row 7 form a Swordfish pattern on possibility <2>. All other instances of this possibility in columns 1, 4 and 9 can be removed.
R1C1 - removing <2> from <257> leaving <57>
R4C1 - removing <2> from <268> leaving <68>
R4C9 - removing <2> from <268> leaving <68>
R5C1 - removing <2> from <1248> leaving <148>
R5C9 - removing <2> from <2348> leaving <348>
R9C4 - removing <2> from <1237> leaving <137>
R4C7 is the only square in row 4 that can be <2>
R9C7 can only be <8>
R5C8 can only be <3>
R9C8 can only be <2>
R1C7 can only be <4>
R9C5 can only be <4>
R1C8 can only be <8>
R1C3 can only be <5>
R3C9 can only be <2>
R3C1 can only be <4>
R5C5 can only be <2>
R1C1 can only be <7>
R9C3 can only be <6>
R5C2 can only be <1>
R6C4 can only be <1>
R6C6 can only be <4>
R6C9 can only be <6>
R6C1 can only be <2>
R4C9 can only be <8>
R4C3 can only be <4>
R1C2 can only be <2>
R8C1 can only be <3>
R4C1 can only be <6>
R5C9 can only be <4>
R5C1 can only be <8>
R9C2 can only be <7>
R8C5 can only be <6>
R8C9 can only be <7>
R7C1 can only be <1>
R1C5 can only be <3>
R7C9 can only be <3>
R9C4 can only be <3>
R9C6 can only be <1>
R4C4 can only be <7>
R9C1 can only be <5>
R7C6 can only be <7>
R1C6 can only be <6>
R4C6 can only be <3>
R7C4 can only be <2>
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