The full reasoning can be found below the Sudoku.
Jul 03 - Super Hard
Puzzle Copyright © Kevin Stone
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Reasoning
R4C2 is the only square in row 4 that can be <6>
R4C5 is the only square in row 4 that can be <9>
R4C1 is the only square in row 4 that can be <5>
R5C9 is the only square in row 5 that can be <3>
R3C8 is the only square in row 3 that can be <3>
R5C1 is the only square in row 5 that can be <7>
R6C1 can only be <2>
R6C2 can only be <3>
R6C9 can only be <4>
R3C1 can only be <1>
R6C5 can only be <5>
R6C8 can only be <7>
R7C1 can only be <8>
R7C2 is the only square in column 2 that can be <1>
R9C2 is the only square in column 2 that can be <7>
Squares R2C5 and R2C7 in row 2 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.
R2C4 - removing <46> from <24569> leaving <259>
R2C6 - removing <4> from <2459> leaving <259>
Squares R7C3 and R8C3 in column 3 form a simple naked pair. These 2 squares both contain the 2 possibilities <35>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the column.
R2C3 - removing <5> from <259> leaving <29>
R3C3 - removing <5> from <259> leaving <29>
Intersection of row 2 with block 2. The value <5> 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.
R1C4 - removing <5> from <145> leaving <14>
R1C6 - removing <5> from <1458> leaving <148>
R3C4 - removing <5> from <245679> leaving <24679>
R3C6 - removing <5> from <24589> leaving <2489>
Squares R1C6 and R1C8 in row 1 and R9C6 and R9C8 in row 9 form a Simple X-Wing pattern on possibility <8>. All other instances of this possibility in columns 6 and 8 can be removed.
R3C6 - removing <8> from <2489> leaving <249>
R4C8 - removing <8> from <28> leaving <2>
R8C6 - removing <8> from <1358> leaving <135>
R4C9 can only be <8>
R3C9 can only be <5>
R3C2 can only be <4>
R7C9 can only be <2>
R1C2 can only be <5>
Squares R3C3 and R3C6 in row 3 form a simple naked pair. These 2 squares both contain the 2 possibilities <29>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the row.
R3C4 - removing <29> from <2679> leaving <67>
Squares R3C3, R3C6, R2C3 and R2C6 form a Type-1 Unique Rectangle on <29>.
R2C6 - removing <29> from <259> leaving <5>
Squares R3C7 (XY), R3C4 (XZ) and R8C7 (YZ) form an XY-Wing pattern on <7>. All squares that are buddies of both the XZ and YZ squares cannot be <7>.
R8C4 - removing <7> from <157> leaving <15>
Squares R1C4<14>, R8C4<15> and R9C4<45> in column 4 form a comprehensive naked triplet. These 3 squares can only contain the 3 possibilities <145>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the column.
R5C4 - removing <14> from <124> leaving <2>
R7C4 - removing <45> from <45679> leaving <679>
R2C4 can only be <9>
R2C3 can only be <2>
R3C6 can only be <2>
R3C3 can only be <9>
R7C6 is the only square in row 7 that can be <9>
R7C3 is the only square in row 7 that can be <3>
R8C3 can only be <5>
R8C4 can only be <1>
R8C6 can only be <3>
R1C4 can only be <4>
R1C8 can only be <8>
R9C4 can only be <5>
R2C5 can only be <6>
R1C6 can only be <1>
R3C7 can only be <6>
R2C7 can only be <4>
R3C4 can only be <7>
R7C7 can only be <7>
R3C5 can only be <8>
R7C4 can only be <6>
R8C5 can only be <7>
R7C5 can only be <4>
R8C7 can only be <8>
R9C8 can only be <4>
R9C6 can only be <8>
R7C8 can only be <5>
R5C6 can only be <4>
R5C5 can only be <1>
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