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The full reasoning can be found below the Sudoku.
Nov 05 - Very Hard
Puzzle Copyright © Kevin Stone
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Reasoning
R4C9 can only be <5>
R6C2 can only be <4>
R9C4 can only be <6>
R1C4 can only be <4>
R2C4 can only be <7>
R8C4 can only be <9>
R5C4 can only be <3>
R5C6 is the only square in row 5 that can be <4>
R6C9 is the only square in row 6 that can be <1>
R6C5 is the only square in row 6 that can be <7>
R5C9 is the only square in row 5 that can be <7>
R5C8 is the only square in row 5 that can be <8>
R7C7 is the only square in row 7 that can be <7>
R7C3 is the only square in row 7 that can be <9>
R8C6 is the only square in row 8 that can be <7>
R9C5 is the only square in row 9 that can be <1>
Squares R4C5 and R5C5 in column 5 form a simple naked pair. These 2 squares both contain the 2 possibilities <69>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the column.
R1C5 - removing <6> from <2568> leaving <258>
R2C5 - removing <6> from <2568> leaving <258>
Squares R4C8 and R6C8 in column 8 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.
R2C8 - removing <6> from <256> leaving <25>
R2C6 is the only square in row 2 that can be <6>
Intersection of column 3 with block 1. The value <6> only appears in one or more of squares R1C3, R2C3 and R3C3 of column 3. These squares are the ones that intersect with block 1. Thus, the other (non-intersecting) squares of block 1 cannot contain this value.
R3C1 - removing <6> from <2568> leaving <258>
Squares R2C2 and R2C5 in row 2 and R8C2 and R8C5 in row 8 form a Simple X-Wing pattern on possibility <8>. All other instances of this possibility in columns 2 and 5 can be removed.
R1C5 - removing <8> from <258> leaving <25>
Squares R1C6 and R1C7 in row 1 and R9C6 and R9C7 in row 9 form a Simple X-Wing pattern on possibility <8>. All other instances of this possibility in columns 6 and 7 can be removed.
R3C7 - removing <8> from <568> leaving <56>
Squares R6C1, R6C8, R4C1 and R4C8 form a Type-1 Unique Rectangle on <36>.
R4C1 - removing <36> from <236> leaving <2>
R4C2 can only be <9>
R7C1 can only be <8>
R4C5 can only be <6>
R5C2 can only be <5>
R4C8 can only be <3>
R5C5 can only be <9>
R6C8 can only be <6>
R5C1 can only be <6>
R6C1 can only be <3>
R7C9 can only be <2>
R3C1 can only be <5>
R8C2 can only be <2>
R3C9 can only be <8>
R8C8 can only be <5>
R8C5 can only be <8>
R2C2 can only be <8>
R9C3 can only be <5>
R9C6 can only be <2>
R2C8 can only be <2>
R9C7 can only be <8>
R1C6 can only be <8>
R2C5 can only be <5>
R3C7 can only be <6>
R3C3 can only be <2>
R1C7 can only be <5>
R1C5 can only be <2>
R1C3 can only be <6>
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