The full reasoning can be found below the Sudoku.
Jan 31 - Hard
Puzzle Copyright © Kevin Stone
www.brainbashers.com
Reasoning
R1C8 is the only square in row 1 that can be <2>
R3C5 is the only square in row 3 that can be <8>
R4C8 is the only square in row 4 that can be <5>
R4C3 is the only square in row 4 that can be <8>
R4C1 is the only square in row 4 that can be <6>
R6C2 can only be <4>
R6C6 can only be <3>
R6C5 can only be <2>
R2C6 can only be <4>
R1C9 is the only square in row 1 that can be <4>
R1C7 is the only square in row 1 that can be <7>
R5C7 can only be <3>
R5C9 can only be <7>
R5C5 is the only square in row 5 that can be <1>
R9C5 is the only square in row 9 that can be <5>
R9C3 is the only square in row 9 that can be <7>
R7C5 is the only square in row 7 that can be <7>
Squares R8C6 and R9C6 in block 8 form a simple naked pair. These 2 squares both contain the 2 possibilities <89>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the block.
R8C4 - removing <9> from <349> leaving <34>
R8C5 - removing <9> from <349> leaving <34>
Squares R8C4 and R8C5 in row 8 form a simple naked pair. These 2 squares both contain the 2 possibilities <34>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the row.
R8C1 - removing <34> from <1349> leaving <19>
R8C9 - removing <3> from <3689> leaving <689>
Intersection of row 3 with block 1. The values <49> 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 these values.
R1C2 - removing <9> from <169> leaving <16>
Intersection of row 3 with block 3. The value <3> only appears in one or more of squares R3C7, R3C8 and R3C9 of row 3. These squares are the ones that intersect with block 3. Thus, the other (non-intersecting) squares of block 3 cannot contain this value.
R2C9 - removing <3> from <356> leaving <56>
Intersection of row 8 with block 9. The value <6> only appears in one or more of squares R8C7, R8C8 and R8C9 of row 8. These squares are the ones that intersect with block 9. Thus, the other (non-intersecting) squares of block 9 cannot contain this value.
R7C7 - removing <6> from <568> leaving <58>
R7C8 - removing <6> from <36> leaving <3>
R7C9 - removing <6> from <35689> leaving <3589>
R9C8 can only be <1>
R3C8 can only be <6>
R2C9 can only be <5>
R3C9 can only be <3>
R3C7 can only be <1>
R3C2 can only be <9>
R3C3 can only be <4>
R9C2 can only be <8>
R3C1 can only be <5>
R9C6 can only be <9>
R7C2 can only be <6>
R9C1 can only be <3>
R8C6 can only be <8>
R7C3 can only be <9>
R1C2 can only be <1>
R7C1 can only be <4>
R7C9 can only be <8>
R5C3 can only be <2>
R8C1 can only be <1>
R7C7 can only be <5>
R6C9 can only be <6>
R8C7 can only be <6>
R2C1 can only be <2>
R8C9 can only be <9>
R6C7 can only be <8>
R1C4 can only be <9>
R1C5 can only be <6>
R4C4 can only be <4>
R2C5 can only be <3>
R2C3 can only be <6>
R5C1 can only be <9>
R2C4 can only be <1>
R8C5 can only be <4>
R4C5 can only be <9>
R8C4 can only be <3>
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