The full reasoning can be found below the Sudoku.
Jun 10 - Hard
Puzzle Copyright © Kevin Stone
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Reasoning
R8C6 is the only square in row 8 that can be <1>
R5C5 is the only square in row 5 that can be <1>
R7C3 is the only square in row 7 that can be <1>
R8C4 is the only square in row 8 that can be <9>
R4C6 is the only square in row 4 that can be <9>
R9C7 is the only square in row 9 that can be <7>
R5C8 is the only square in column 8 that can be <5>
Squares R6C3 and R6C5 in row 6 form a simple naked pair. These 2 squares both contain the 2 possibilities <56>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the row.
R6C4 - removing <5> from <2345> leaving <234>
R6C6 - removing <56> from <23456> leaving <234>
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.
R1C7 - removing <3> from <369> leaving <69>
R1C9 - removing <3> from <349> leaving <49>
Intersection of block 4 with row 5. The value <3> only appears in one or more of squares R5C1, R5C2 and R5C3 of block 4. These squares are the ones that intersect with row 5. Thus, the other (non-intersecting) squares of row 5 cannot contain this value.
R5C4 - removing <3> from <2378> leaving <278>
R5C6 - removing <3> from <236> leaving <26>
R5C9 - removing <3> from <238> leaving <28>
Intersection of block 8 with row 9. The value <2> only appears in one or more of squares R9C4, R9C5 and R9C6 of block 8. These squares are the ones that intersect with row 9. Thus, the other (non-intersecting) squares of row 9 cannot contain this value.
R9C3 - removing <2> from <2456> leaving <456>
R9C9 - removing <2> from <248> leaving <48>
R3C3 is the only square in column 3 that can be <2>
R2C8 is the only square in row 2 that can be <2>
R8C8 can only be <3>
R8C2 can only be <2>
R7C8 can only be <4>
R3C8 can only be <7>
R9C9 can only be <8>
R5C9 can only be <2>
R5C6 can only be <6>
R7C9 can only be <9>
R6C7 can only be <3>
R4C7 can only be <8>
R7C7 can only be <2>
R1C9 can only be <4>
R3C9 can only be <3>
R5C1 can only be <3>
R2C6 can only be <4>
R6C5 can only be <5>
R6C3 can only be <6>
R3C5 can only be <6>
R4C5 can only be <7>
R7C5 can only be <8>
R2C4 can only be <7>
R6C6 can only be <2>
R3C2 can only be <5>
R3C7 can only be <9>
R1C7 can only be <6>
R4C3 can only be <5>
R4C4 can only be <3>
R5C4 can only be <8>
R5C2 can only be <7>
R7C1 can only be <5>
R2C2 can only be <6>
R6C4 can only be <4>
R9C6 can only be <5>
R7C2 can only be <3>
R3C1 can only be <4>
R9C3 can only be <4>
R9C1 can only be <6>
R9C4 can only be <2>
R1C6 can only be <3>
R1C1 can only be <9>
R1C4 can only be <5>
R1C3 can only be <7>
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