The full reasoning can be found below the Sudoku.
Apr 29 - Very Hard
Puzzle Copyright © Kevin Stone
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Reasoning
R1C1 can only be <2>
R5C1 can only be <8>
R9C9 can only be <9>
R9C1 can only be <3>
R9C5 can only be <2>
R2C5 is the only square in row 2 that can be <3>
R2C2 is the only square in row 2 that can be <8>
R2C8 is the only square in row 2 that can be <1>
R3C2 is the only square in row 3 that can be <1>
R4C6 is the only square in row 4 that can be <1>
R7C8 is the only square in row 7 that can be <3>
R8C7 is the only square in row 8 that can be <8>
R8C5 is the only square in row 8 that can be <9>
R5C4 is the only square in row 5 that can be <9>
Squares R7C4 and R7C6 in row 7 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.
R7C2 - removing <5> from <457> leaving <47>
R7C3 - removing <5> from <2457> leaving <247>
Squares R2C3 and R3C3 in column 3 form a simple naked pair. These 2 squares both contain the 2 possibilities <49>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the column.
R7C3 - removing <4> from <247> leaving <27>
R8C3 - removing <4> from <245> leaving <25>
Squares R1C5 and R6C5 in column 5 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.
R4C5 - removing <5> from <567> leaving <67>
R5C5 - removing <45> from <4567> leaving <67>
Squares R5C9 and R6C5 form a remote naked pair. <45> can be removed from any square that is common to their groups.
R6C7 - removing <45> from <245> leaving <2>
R5C6 - removing <45> from <245> leaving <2>
R7C7 can only be <4>
R7C2 can only be <7>
R2C7 can only be <9>
R8C8 can only be <2>
R8C3 can only be <5>
R2C3 can only be <4>
R7C3 can only be <2>
R5C2 can only be <5>
R8C2 can only be <4>
R6C3 can only be <3>
R3C3 can only be <9>
R5C9 can only be <4>
R5C8 can only be <6>
R1C9 can only be <5>
R4C3 can only be <7>
R1C5 can only be <4>
R3C7 can only be <6>
R3C8 can only be <4>
R4C7 can only be <5>
R3C6 can only be <5>
R4C5 can only be <6>
R5C5 can only be <7>
R4C4 can only be <3>
R6C5 can only be <5>
R3C4 can only be <2>
R7C6 can only be <8>
R6C4 can only be <8>
R7C4 can only be <5>
R6C6 can only be <4>
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