The full reasoning can be found below the Sudoku.
Apr 08 - Hard
Puzzle Copyright © Kevin Stone
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Reasoning
R4C4 can only be <8>
R3C4 can only be <7>
R1C5 can only be <3>
R1C9 can only be <9>
R2C5 can only be <1>
R3C6 can only be <8>
R5C4 is the only square in row 5 that can be <5>
R6C4 can only be <4>
R7C4 can only be <6>
R5C5 is the only square in row 5 that can be <6>
R5C8 is the only square in row 5 that can be <9>
R4C5 is the only square in row 4 that can be <9>
R6C7 is the only square in row 6 that can be <5>
R7C3 is the only square in row 7 that can be <5>
R8C7 is the only square in row 8 that can be <6>
R2C3 is the only square in row 2 that can be <6>
R3C9 is the only square in row 3 that can be <6>
R8C5 is the only square in column 5 that can be <4>
Intersection of row 2 with block 3. The value <3> only appears in one or more of squares R2C7, R2C8 and R2C9 of row 2. These squares are the ones that intersect with block 3. Thus, the other (non-intersecting) squares of block 3 cannot contain this value.
R3C7 - removing <3> from <134> leaving <14>
R3C8 - removing <3> from <123> leaving <12>
Intersection of row 8 with block 7. The value <7> only appears in one or more of squares R8C1, R8C2 and R8C3 of row 8. These squares are the ones that intersect with block 7. Thus, the other (non-intersecting) squares of block 7 cannot contain this value.
R7C1 - removing <7> from <1347> leaving <134>
R7C2 - removing <7> from <479> leaving <49>
R9C1 - removing <7> from <178> leaving <18>
R9C3 - removing <7> from <179> leaving <19>
Intersection of column 2 with block 1. The value <2> only appears in one or more of squares R1C2, R2C2 and R3C2 of column 2. These squares are the ones that intersect with block 1. Thus, the other (non-intersecting) squares of block 1 cannot contain this value.
R3C3 - removing <2> from <2349> leaving <349>
Intersection of column 3 with block 1. The value <4> only appears in one or more of squares R1C3, R2C3 and R3C3 of column 3. These squares are the ones that intersect with block 1. Thus, the other (non-intersecting) squares of block 1 cannot contain this value.
R1C1 - removing <4> from <478> leaving <78>
R3C1 - removing <4> from <34> leaving <3>
R3C2 - removing <4> from <249> leaving <29>
R8C3 is the only square in column 3 that can be <3>
R8C8 can only be <8>
R8C2 can only be <7>
R5C2 can only be <4>
R7C2 can only be <9>
R3C2 can only be <2>
R9C3 can only be <1>
R9C1 can only be <8>
R9C9 can only be <2>
R4C3 can only be <2>
R7C1 can only be <4>
R9C5 can only be <7>
R3C8 can only be <1>
R2C2 can only be <8>
R3C7 can only be <4>
R7C8 can only be <3>
R6C3 can only be <7>
R6C5 can only be <2>
R1C3 can only be <4>
R5C1 can only be <1>
R6C6 can only be <1>
R4C6 can only be <3>
R7C9 can only be <1>
R2C8 can only be <2>
R7C7 can only be <7>
R5C9 can only be <3>
R1C1 can only be <7>
R9C7 can only be <9>
R7C6 can only be <2>
R1C7 can only be <8>
R3C3 can only be <9>
R2C7 can only be <3>
R4C7 can only be <1>
R5C6 can only be <7>
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