The full reasoning can be found below the Sudoku.
Apr 24 - Super Hard
Puzzle Copyright © Kevin Stone
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Reasoning
R3C7 can only be <3>
R2C5 is the only square in row 2 that can be <3>
R3C2 is the only square in row 3 that can be <9>
R3C3 is the only square in row 3 that can be <1>
R3C8 is the only square in row 3 that can be <5>
R1C9 can only be <2>
R1C5 can only be <6>
R1C1 can only be <5>
R3C5 is the only square in row 3 that can be <8>
R5C8 is the only square in row 5 that can be <6>
R5C1 is the only square in row 5 that can be <3>
R4C8 is the only square in row 4 that can be <3>
R7C2 is the only square in row 7 that can be <6>
R2C2 can only be <8>
R2C1 can only be <6>
R8C5 is the only square in row 8 that can be <4>
R8C9 is the only square in row 8 that can be <5>
Squares R5C3 and R5C7 in row 5 form a simple naked pair. These 2 squares both contain the 2 possibilities <78>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the row.
R5C2 - removing <7> from <1257> leaving <125>
R5C5 - removing <7> from <2579> leaving <259>
R5C9 - removing <78> from <14789> leaving <149>
Squares R7C3 and R7C7 in row 7 form a simple naked pair. These 2 squares both contain the 2 possibilities <78>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the row.
R7C8 - removing <7> from <179> leaving <19>
Intersection of row 6 with block 6. The value <4> only appears in one or more of squares R6C7, R6C8 and R6C9 of row 6. These squares are the ones that intersect with block 6. Thus, the other (non-intersecting) squares of block 6 cannot contain this value.
R5C9 - removing <4> from <149> leaving <19>
Intersection of column 8 with block 9. The value <1> only appears in one or more of squares R7C8, R8C8 and R9C8 of column 8. These squares are the ones that intersect with block 9. Thus, the other (non-intersecting) squares of block 9 cannot contain this value.
R9C9 - removing <1> from <189> leaving <89>
Squares R2C8, R2C9, R6C8 and R6C9 form a Type-3 Unique Rectangle on <47>. Upon close inspection, it is clear that:
(R6C8 or R6C9)<89> and R6C1<89> form a naked pair on <89> in row 6. No other squares in the row can contain these possibilities
R6C5 - removing <9> from <579> leaving <57>
Squares R6C2 and R6C5 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.
R6C8 - removing <7> from <479> leaving <49>
R6C9 - removing <7> from <4789> leaving <489>
Squares R3C4, R3C6, R5C4 and R5C6 form a Type-4 Unique Rectangle on <24>.
R5C4 - removing <2> from <249> leaving <49>
R5C6 - removing <2> from <245> leaving <45>
Intersection of block 5 with column 5. The values <27> only appears in one or more of squares R4C5, R5C5 and R6C5 of block 5. These squares are the ones that intersect with column 5. Thus, the other (non-intersecting) squares of column 5 cannot contain these values.
R7C5 - removing <2> from <1259> leaving <159>
Squares R6C9 (XYZ), R6C8 (XZ) and R9C9 (YZ) form an XYZ-Wing pattern on <9>. All squares that are buddies of all three squares cannot be <9>.
R4C9 - removing <9> from <179> leaving <17>
R5C9 - removing <9> from <19> leaving <1>
R4C9 can only be <7>
R2C9 can only be <4>
R5C7 can only be <8>
R5C3 can only be <7>
R7C7 can only be <7>
R7C3 can only be <8>
R8C8 can only be <1>
R8C1 can only be <2>
R7C8 can only be <9>
R2C8 can only be <7>
R6C9 can only be <9>
R6C2 can only be <5>
R6C5 can only be <7>
R5C2 can only be <2>
R6C1 can only be <8>
R6C8 can only be <4>
R9C9 can only be <8>
R9C1 can only be <1>
R7C4 can only be <2>
R8C2 can only be <7>
R9C5 can only be <9>
R4C1 can only be <9>
R4C5 can only be <2>
R4C2 can only be <1>
R5C5 can only be <5>
R5C6 can only be <4>
R7C5 can only be <1>
R5C4 can only be <9>
R3C6 can only be <2>
R7C6 can only be <5>
R3C4 can only be <4>
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