The full reasoning can be found below the Sudoku.
Mar 03 - Super Hard
Puzzle Copyright © Kevin Stone
Reasoning
R5C2 is the only square in row 5 that can be <6>
R5C8 is the only square in row 5 that can be <5>
R5C1 is the only square in row 5 that can be <9>
Squares R2C1 and R2C9 in row 2 form a simple naked pair. These 2 squares both contain the 2 possibilities <37>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the row.
R2C3 - removing <37> from <23467> leaving <246>
R2C4 - removing <7> from <2457> leaving <245>
R2C5 - removing <7> from <24579> leaving <2459>
R2C6 - removing <7> from <2679> leaving <269>
Squares R6C2 and R6C3 in row 6 form a simple naked pair. These 2 squares both contain the 2 possibilities <57>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the row.
R6C5 - removing <7> from <178> leaving <18>
R6C8 - removing <7> from <179> leaving <19>
Squares R6C2 and R6C3 in block 4 form a simple naked pair. These 2 squares both contain the 2 possibilities <57>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the block.
R4C2 - removing <7> from <237> leaving <23>
R4C3 - removing <7> from <237> leaving <23>
Squares R4C2 and R4C3 in row 4 form a simple naked pair. These 2 squares both contain the 2 possibilities <23>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the row.
R4C5 - removing <2> from <2478> leaving <478>
Intersection of row 5 with block 5. The values <24> only appears in one or more of squares R5C4, R5C5 and R5C6 of row 5. These squares are the ones that intersect with block 5. Thus, the other (non-intersecting) squares of block 5 cannot contain these values.
R4C5 - removing <4> from <478> leaving <78>
Squares R1C2 and R1C8 in row 1 and R9C2 and R9C8 in row 9 form a Simple X-Wing pattern on possibility <3>. All other instances of this possibility in columns 2 and 8 can be removed.
R4C2 - removing <3> from <23> leaving <2>
R7C2 - removing <3> from <34579> leaving <4579>
R7C8 - removing <3> from <1349> leaving <149>
R4C3 can only be <3>
R7C4 is the only square in row 7 that can be <3>
Squares R1C2 and R2C1 in block 1 form a simple naked pair. These 2 squares both contain the 2 possibilities <37>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the block.
R3C2 - removing <7> from <47> leaving <4>
R3C3 - removing <7> from <2467> leaving <246>
Intersection of row 7 with block 7. The value <5> only appears in one or more of squares R7C1, R7C2 and R7C3 of row 7. These squares are the ones that intersect with block 7. Thus, the other (non-intersecting) squares of block 7 cannot contain this value.
R8C3 - removing <5> from <457> leaving <47>
Squares R1C5 and R1C8 in row 1 and R9C5 and R9C8 in row 9 form a Simple X-Wing pattern on possibility <2>. All other instances of this possibility in columns 5 and 8 can be removed.
R2C5 - removing <2> from <2459> leaving <459>
R3C8 - removing <2> from <127> leaving <17>
R5C5 - removing <2> from <1247> leaving <147>
R8C5 - removing <2> from <12579> leaving <1579>
Squares R3C8<17>, R4C8<47>, R6C8<19> and R7C8<149> in column 8 form a comprehensive naked quad. These 4 squares can only contain the 4 possibilities <1479>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the column.
R1C8 - removing <7> from <237> leaving <23>
R9C8 - removing <9> from <239> leaving <23>
Squares R6C2, R6C3, R7C2 and R7C3 form a Type-3 Unique Rectangle on <57>. Upon close inspection, it is clear that:
(R7C2 or R7C3)<49>, R7C8<149> and R7C7<149> form a naked triplet on <149> in row 7. No other squares in the row can contain these possibilities
R7C6 - removing <19> from <179> leaving <7>
Squares R3C3 and R3C6 in row 3 form a simple naked pair. These 2 squares both contain the 2 possibilities <26>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the row.
R3C4 - removing <2> from <257> leaving <57>
R3C7 - removing <2> from <125> leaving <15>
Intersection of row 7 with block 9. The value <1> only appears in one or more of squares R7C7, R7C8 and R7C9 of row 7. These squares are the ones that intersect with block 9. Thus, the other (non-intersecting) squares of block 9 cannot contain this value.
R8C7 - removing <1> from <1249> leaving <249>
R8C9 - removing <1> from <13> leaving <3>
R8C1 can only be <7>
R2C9 can only be <7>
R9C8 can only be <2>
R9C5 can only be <9>
R1C8 can only be <3>
R1C2 can only be <7>
R2C1 can only be <3>
R5C9 can only be <1>
R3C8 can only be <1>
R3C7 can only be <5>
R6C8 can only be <9>
R5C6 can only be <2>
R6C7 can only be <8>
R7C8 can only be <4>
R7C3 can only be <5>
R4C8 can only be <7>
R8C7 can only be <9>
R8C3 can only be <4>
R7C7 can only be <1>
R9C2 can only be <3>
R1C5 can only be <2>
R6C2 can only be <5>
R3C6 can only be <6>
R3C3 can only be <2>
R2C6 can only be <9>
R3C4 can only be <7>
R2C7 can only be <2>
R4C5 can only be <8>
R8C6 can only be <1>
R6C3 can only be <7>
R7C2 can only be <9>
R6C5 can only be <1>
R4C7 can only be <4>
R8C5 can only be <5>
R2C3 can only be <6>
R5C4 can only be <4>
R5C5 can only be <7>
R2C4 can only be <5>
R8C4 can only be <2>
R2C5 can only be <4>
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