The full reasoning can be found below the Sudoku.
Apr 16 - Hard
Puzzle Copyright © Kevin Stone
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Reasoning
R4C5 is the only square in row 4 that can be <9>
R5C5 is the only square in row 5 that can be <4>
R5C4 is the only square in row 5 that can be <7>
R5C6 is the only square in row 5 that can be <6>
R2C5 is the only square in column 5 that can be <7>
R7C9 is the only square in column 9 that can be <7>
R9C9 is the only square in column 9 that can be <5>
R5C2 is the only square in block 4 that can be <2>
Intersection of row 9 with block 9. The value <9> only appears in one or more of squares R9C7, R9C8 and R9C9 of row 9. 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 <9> from <1389> leaving <138>
R7C8 - removing <9> from <1389> leaving <138>
R8C7 - removing <9> from <3689> leaving <368>
Intersection of column 8 with block 3. The value <2> only appears in one or more of squares R1C8, R2C8 and R3C8 of column 8. These squares are the ones that intersect with block 3. Thus, the other (non-intersecting) squares of block 3 cannot contain this value.
R2C7 - removing <2> from <23468> leaving <3468>
R3C7 - removing <2> from <124689> leaving <14689>
Intersection of row 2 with block 2. The value <2> only appears in one or more of squares R2C4, R2C5 and R2C6 of row 2. These squares are the ones that intersect with block 2. Thus, the other (non-intersecting) squares of block 2 cannot contain this value.
R1C5 - removing <2> from <1258> leaving <158>
R3C4 - removing <2> from <1256> leaving <156>
R3C6 - removing <2> from <258> leaving <58>
R6C5 is the only square in column 5 that can be <2>
R4C7 is the only square in row 4 that can be <2>
Squares R4C4 and R8C4 in column 4 form a simple naked pair. These 2 squares both contain the 2 possibilities <35>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the column.
R3C4 - removing <5> from <156> leaving <16>
R7C4 - removing <35> from <1235> leaving <12>
Intersection of column 9 with block 3. The values <168> only appears in one or more of squares R1C9, R2C9 and R3C9 of column 9. These squares are the ones that intersect with block 3. Thus, the other (non-intersecting) squares of block 3 cannot contain these values.
R1C8 - removing <18> from <1238> leaving <23>
R2C7 - removing <68> from <3468> leaving <34>
R3C7 - removing <168> from <14689> leaving <49>
R3C8 - removing <18> from <1289> leaving <29>
Intersection of block 4 with column 3. The values <135> only appears in one or more of squares R4C3, R5C3 and R6C3 of block 4. These squares are the ones that intersect with column 3. Thus, the other (non-intersecting) squares of column 3 cannot contain these values.
R1C3 - removing <35> from <3568> leaving <68>
R2C3 - removing <3> from <3468> leaving <468>
R3C3 - removing <5> from <45678> leaving <4678>
R7C3 - removing <35> from <34589> leaving <489>
R8C3 - removing <35> from <356789> leaving <6789>
R2C7 is the only square in row 2 that can be <3>
R1C8 can only be <2>
R3C8 can only be <9>
R3C7 can only be <4>
R2C3 is the only square in row 2 that can be <4>
R3C1 is the only square in row 3 that can be <2>
R3C3 is the only square in row 3 that can be <7>
R7C2 is the only square in row 7 that can be <4>
R8C1 is the only square in row 8 that can be <7>
R9C7 is the only square in row 9 that can be <9>
R9C2 is the only square in row 9 that can be <6>
R3C2 can only be <5>
R3C6 can only be <8>
R1C2 can only be <3>
R2C6 can only be <2>
R1C1 can only be <8>
R2C4 can only be <6>
R1C3 can only be <6>
R9C1 can only be <3>
R1C9 can only be <1>
R1C5 can only be <5>
R3C9 can only be <6>
R2C9 can only be <8>
R3C4 can only be <1>
R7C4 can only be <2>
R7C1 can only be <5>
R8C5 can only be <8>
R8C3 can only be <9>
R8C7 can only be <6>
R9C5 can only be <1>
R9C8 can only be <8>
R5C8 can only be <1>
R7C7 can only be <1>
R5C3 can only be <5>
R7C8 can only be <3>
R6C7 can only be <5>
R6C6 can only be <3>
R5C7 can only be <8>
R7C6 can only be <9>
R7C3 can only be <8>
R4C3 can only be <3>
R6C3 can only be <1>
R8C6 can only be <5>
R4C4 can only be <5>
R8C4 can only be <3>
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