The full reasoning can be found below the Sudoku.
May 02 - Super Hard
Puzzle Copyright © Kevin Stone
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Reasoning
R8C1 is the only square in column 1 that can be <1>
R8C4 is the only square in column 4 that can be <5>
R9C1 is the only square in row 9 that can be <5>
R7C4 is the only square in column 4 that can be <7>
R4C6 is the only square in column 6 that can be <6>
R5C5 can only be <8>
R5C8 can only be <4>
R5C2 can only be <6>
R7C6 is the only square in column 6 that can be <8>
Squares R7C2 and R7C3 in row 7 form a simple naked pair. These 2 squares both contain the 2 possibilities <39>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the row.
R7C7 - removing <3> from <123> leaving <12>
R7C9 - removing <39> from <1239> leaving <12>
Squares R8C5 and R9C5 in column 5 form a simple naked pair. These 2 squares both contain the 2 possibilities <36>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the column.
R2C5 - removing <3> from <2359> leaving <259>
R4C5 - removing <3> from <13> leaving <1>
R6C5 - removing <3> from <139> leaving <19>
R6C5 can only be <9>
R6C4 can only be <3>
R3C4 can only be <9>
R4C9 is the only square in row 4 that can be <3>
R8C9 is the only square in column 9 that can be <8>
Squares R6C7 and R7C7 in column 7 form a simple naked pair. These 2 squares both contain the 2 possibilities <12>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the column.
R1C7 - removing <2> from <2467> leaving <467>
R3C7 - removing <2> from <246> leaving <46>
Squares R7C2 and R7C3 in block 7 form a simple naked pair. These 2 squares both contain the 2 possibilities <39>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the block.
R8C2 - removing <3> from <347> leaving <47>
R9C3 - removing <39> from <3479> leaving <47>
Intersection of column 1 with block 1. The value <7> only appears in one or more of squares R1C1, R2C1 and R3C1 of column 1. These squares are the ones that intersect with block 1. Thus, the other (non-intersecting) squares of block 1 cannot contain this value.
R1C2 - removing <7> from <24579> leaving <2459>
R1C3 - removing <7> from <4679> leaving <469>
R2C2 - removing <7> from <234579> leaving <23459>
R2C3 - removing <7> from <3479> leaving <349>
Squares R4C2<27>, R6C2<24> and R8C2<47> in column 2 form a comprehensive naked triplet. These 3 squares can only contain the 3 possibilities <247>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the column.
R1C2 - removing <24> from <2459> leaving <59>
R2C2 - removing <24> from <23459> leaving <359>
Intersection of column 2 with block 4. The value <2> only appears in one or more of squares R4C2, R5C2 and R6C2 of column 2. These squares are the ones that intersect with block 4. Thus, the other (non-intersecting) squares of block 4 cannot contain this value.
R6C1 - removing <2> from <248> leaving <48>
Squares R8C5, R9C5, R8C7 and R9C7 form a Type-4 Unique Rectangle on <36>.
R8C7 - removing <6> from <3467> leaving <347>
R9C7 - removing <6> from <3467> leaving <347>
Intersection of column 7 with block 3. The value <6> only appears in one or more of squares R1C7, R2C7 and R3C7 of column 7. These squares are the ones that intersect with block 3. Thus, the other (non-intersecting) squares of block 3 cannot contain this value.
R3C8 - removing <6> from <26> leaving <2>
R4C8 can only be <8>
R4C3 can only be <7>
R6C8 can only be <1>
R6C7 can only be <2>
R4C2 can only be <2>
R9C3 can only be <4>
R6C2 can only be <4>
R7C7 can only be <1>
R7C9 can only be <2>
R9C9 can only be <9>
R8C2 can only be <7>
R1C9 can only be <4>
R2C9 can only be <1>
R3C7 can only be <6>
R1C7 can only be <7>
R6C1 can only be <8>
R8C8 can only be <6>
R8C5 can only be <3>
R9C8 can only be <7>
R9C7 can only be <3>
R2C8 can only be <9>
R1C1 can only be <2>
R2C3 can only be <3>
R3C1 can only be <4>
R8C7 can only be <4>
R9C5 can only be <6>
R1C5 can only be <5>
R1C2 can only be <9>
R2C5 can only be <2>
R2C2 can only be <5>
R2C6 can only be <4>
R3C3 can only be <8>
R7C3 can only be <9>
R2C1 can only be <7>
R3C6 can only be <3>
R7C2 can only be <3>
R1C3 can only be <6>
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