The full reasoning can be found below the Sudoku.
Mar 28 - Very Hard
Puzzle Copyright © Kevin Stone
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Reasoning
R1C7 is the only square in row 1 that can be <2>
R2C2 is the only square in row 2 that can be <7>
R5C4 is the only square in row 5 that can be <9>
R5C6 is the only square in row 5 that can be <7>
R6C5 is the only square in row 6 that can be <2>
R7C8 is the only square in row 7 that can be <1>
R8C2 is the only square in row 8 that can be <2>
R8C4 is the only square in row 8 that can be <7>
R9C5 is the only square in row 9 that can be <1>
R5C2 is the only square in row 5 that can be <1>
R4C6 is the only square in row 4 that can be <1>
R3C2 is the only square in column 2 that can be <9>
R7C2 is the only square in column 2 that can be <5>
R2C6 is the only square in column 6 that can be <3>
R8C7 is the only square in column 7 that can be <3>
R5C1 is the only square in block 4 that can be <8>
R1C9 is the only square in column 9 that can be <8>
R2C3 is the only square in row 2 that can be <8>
Squares R4C2 and R4C4 in row 4 form a simple naked pair. These 2 squares both contain the 2 possibilities <46>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the row.
R4C5 - removing <46> from <3468> leaving <38>
R4C8 - removing <4> from <348> leaving <38>
Squares R8C5 and R8C6 in row 8 form a simple naked pair. These 2 squares both contain the 2 possibilities <58>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the row.
R8C8 - removing <5> from <459> leaving <49>
Intersection of row 2 with block 2. The value <4> 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 <4> from <456> leaving <56>
Intersection of column 5 with block 2. The value <6> only appears in one or more of squares R1C5, R2C5 and R3C5 of column 5. These squares are the ones that intersect with block 2. Thus, the other (non-intersecting) squares of block 2 cannot contain this value.
R2C4 - removing <6> from <456> leaving <45>
Squares R4C2, R4C4, R6C2 and R6C4 form a Type-1 Unique Rectangle on <46>.
R6C4 - removing <46> from <456> leaving <5>
R6C6 can only be <8>
R2C4 can only be <4>
R6C8 can only be <4>
R8C6 can only be <5>
R4C5 can only be <3>
R6C2 can only be <6>
R8C8 can only be <9>
R8C5 can only be <8>
R8C3 can only be <4>
R9C7 can only be <5>
R9C9 can only be <7>
R2C7 can only be <9>
R9C1 can only be <6>
R7C9 can only be <4>
R4C4 can only be <6>
R4C2 can only be <4>
R4C8 can only be <8>
R5C5 can only be <4>
R7C1 can only be <7>
R1C3 can only be <6>
R9C3 can only be <9>
R3C1 can only be <5>
R1C5 can only be <5>
R1C1 can only be <4>
R2C5 can only be <6>
R2C8 can only be <5>
R5C8 can only be <3>
R3C9 can only be <3>
R3C8 can only be <6>
R5C9 can only be <5>
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