The full reasoning can be found below the Sudoku.
Apr 25 - Very Hard
Puzzle Copyright © Kevin Stone
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Reasoning
R5C5 can only be <6>
R9C4 can only be <6>
R9C6 can only be <7>
R1C4 can only be <2>
R8C6 can only be <9>
R2C4 can only be <3>
R8C4 can only be <1>
R3C2 is the only square in row 3 that can be <3>
R4C1 is the only square in row 4 that can be <3>
R4C8 is the only square in row 4 that can be <5>
R7C2 is the only square in row 7 that can be <1>
R7C3 is the only square in row 7 that can be <9>
R8C8 is the only square in row 8 that can be <2>
R8C5 is the only square in row 8 that can be <3>
R7C5 can only be <8>
R7C7 can only be <7>
R7C8 can only be <3>
R8C1 is the only square in column 1 that can be <7>
R9C8 is the only square in column 8 that can be <4>
R9C2 can only be <8>
R1C8 is the only square in row 1 that can be <8>
Squares R3C3 and R8C3 in column 3 form a simple naked pair. These 2 squares both contain the 2 possibilities <45>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the column.
R2C3 - removing <45> from <2458> leaving <28>
Squares R3C8 and R6C8 in column 8 form a simple naked pair. These 2 squares both contain the 2 possibilities <69>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the column.
R2C8 - removing <69> from <1679> leaving <17>
Intersection of row 3 with block 3. The value <6> 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.
R2C7 - removing <6> from <156> leaving <15>
R2C9 - removing <6> from <679> leaving <79>
Squares R2C9 and R4C9 in column 9 form a simple naked pair. These 2 squares both contain the 2 possibilities <79>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the column.
R6C9 - removing <9> from <689> leaving <68>
Squares R1C2, R1C6, R2C2 and R2C6 form a Type-1 Unique Rectangle on <56>.
R2C2 - removing <56> from <2456> leaving <24>
R2C6 is the only square in row 2 that can be <6>
R1C6 can only be <5>
R1C2 can only be <6>
R2C7 is the only square in row 2 that can be <5>
R3C7 can only be <6>
R3C8 can only be <9>
R8C7 can only be <8>
R3C5 can only be <4>
R6C8 can only be <6>
R2C9 can only be <7>
R6C9 can only be <8>
R6C1 can only be <4>
R8C9 can only be <6>
R5C7 can only be <1>
R2C8 can only be <1>
R4C9 can only be <9>
R3C3 can only be <5>
R2C5 can only be <9>
R4C2 can only be <7>
R5C8 can only be <7>
R5C2 can only be <2>
R6C2 can only be <9>
R2C1 can only be <8>
R2C3 can only be <2>
R2C2 can only be <4>
R5C3 can only be <8>
R8C3 can only be <4>
R8C2 can only be <5>
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