The full reasoning can be found below the Sudoku.
Mar 25 - Hard
Puzzle Copyright © Kevin Stone
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Reasoning
R2C2 can only be <8>
R9C5 is the only square in row 9 that can be <2>
R2C5 can only be <9>
R8C2 is the only square in column 2 that can be <6>
R8C8 can only be <9>
R2C8 is the only square in column 8 that can be <2>
R3C7 is the only square in block 3 that can be <3>
Squares R6C2 and R6C5 in row 6 form a simple naked pair. These 2 squares both contain the 2 possibilities <57>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the row.
R6C3 - removing <57> from <23579> leaving <239>
R6C4 - removing <5> from <24589> leaving <2489>
R6C6 - removing <7> from <24789> leaving <2489>
R6C7 - removing <57> from <4578> leaving <48>
R4C7 is the only square in column 7 that can be <7>
R5C9 is the only square in block 6 that can be <5>
R6C7 is the only square in block 6 that can be <8>
Squares R6C5 and R8C5 in column 5 form a simple naked pair. These 2 squares both contain the 2 possibilities <57>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the column.
R4C5 - removing <5> from <156> leaving <16>
Intersection of row 1 with block 1. The value <2> only appears in one or more of squares R1C1, R1C2 and R1C3 of row 1. These squares are the ones that intersect with block 1. Thus, the other (non-intersecting) squares of block 1 cannot contain this value.
R3C1 - removing <2> from <279> leaving <79>
R3C3 - removing <2> from <1279> leaving <179>
Intersection of row 8 with block 8. The values <578> only appears in one or more of squares R8C4, R8C5 and R8C6 of row 8. These squares are the ones that intersect with block 8. Thus, the other (non-intersecting) squares of block 8 cannot contain these values.
R7C4 - removing <58> from <3589> leaving <39>
R7C6 - removing <78> from <3789> leaving <39>
Squares R7C4 and R7C6 in row 7 form a simple naked pair. These 2 squares both contain the 2 possibilities <39>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the row.
R7C1 - removing <3> from <378> leaving <78>
R7C3 - removing <3> from <357> leaving <57>
R9C1 is the only square in column 1 that can be <3>
R9C3 can only be <5>
R9C7 can only be <4>
R7C3 can only be <7>
R9C9 can only be <8>
R1C7 can only be <6>
R7C9 can only be <6>
R1C5 can only be <1>
R7C7 can only be <5>
R3C9 can only be <9>
R3C1 can only be <7>
R1C9 can only be <4>
R7C1 can only be <8>
R3C3 can only be <1>
R4C5 can only be <6>
R3C4 can only be <2>
R5C1 can only be <2>
R3C6 can only be <6>
R4C8 can only be <3>
R4C3 can only be <9>
R6C8 can only be <4>
R1C1 can only be <9>
R6C4 can only be <9>
R5C8 can only be <6>
R1C3 can only be <2>
R4C6 can only be <8>
R6C3 can only be <3>
R8C6 can only be <7>
R6C6 can only be <2>
R7C4 can only be <3>
R7C6 can only be <9>
R2C4 can only be <4>
R8C5 can only be <5>
R5C6 can only be <4>
R2C6 can only be <3>
R5C4 can only be <1>
R5C2 can only be <7>
R4C4 can only be <5>
R8C4 can only be <8>
R6C5 can only be <7>
R4C2 can only be <1>
R6C2 can only be <5>
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