Dec 07 - Very Hard
Puzzle Copyright © Kevin Stone
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Reasoning
R1C9 can only be <3>
R2C6 can only be <1>
R9C9 can only be <9>
R2C4 can only be <8>
R4C6 can only be <5>
R4C2 can only be <6>
R4C8 can only be <2>
R3C9 can only be <5>
R4C4 can only be <1>
R3C5 can only be <2>
R7C9 can only be <4>
R4C5 can only be <8>
R5C6 is the only square in row 5 that can be <4>
R6C4 is the only square in row 6 that can be <2>
R6C5 is the only square in row 6 that can be <6>
R8C3 is the only square in row 8 that can be <8>
R1C3 can only be <1>
R8C7 is the only square in row 8 that can be <2>
R7C3 is the only square in row 7 that can be <2>
Squares R7C1 and R7C5 in row 7 form a simple naked pair. These 2 squares both contain the 2 possibilities <79>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the row.
R7C2 - removing <79> from <1379> leaving <13>
R7C7 - removing <7> from <1357> leaving <135>
R7C8 - removing <7> from <1357> leaving <135>
Intersection of block 8 with row 8. The value <3> only appears in one or more of squares R8C4, R8C5 and R8C6 of block 8. These squares are the ones that intersect with row 8. Thus, the other (non-intersecting) squares of row 8 cannot contain this value.
R8C2 - removing <3> from <1379> leaving <179>
R8C8 - removing <3> from <137> leaving <17>
Squares R2C8<79>, R3C8<19> and R8C8<17> in column 8 form a comprehensive naked triplet. These 3 squares can only contain the 3 possibilities <179>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the column.
R7C8 - removing <1> from <135> leaving <35>
Squares R1C1 and R1C7 in row 1 and R9C1 and R9C7 in row 9 form a Simple X-Wing pattern on possibility <7>. All other instances of this possibility in columns 1 and 7 can be removed.
R2C7 - removing <7> from <67> leaving <6>
R7C1 - removing <7> from <79> leaving <9>
R7C5 can only be <7>
R5C5 can only be <9>
R8C4 can only be <3>
R8C6 can only be <9>
R5C4 can only be <7>
R6C6 can only be <3>
R5C3 can only be <5>
R6C8 can only be <5>
R6C2 can only be <9>
R7C8 can only be <3>
R5C7 can only be <3>
R7C2 can only be <1>
R9C7 can only be <7>
R9C1 can only be <6>
R1C7 can only be <8>
R8C8 can only be <1>
R1C1 can only be <7>
R3C7 can only be <1>
R3C8 can only be <9>
R7C7 can only be <5>
R3C2 can only be <3>
R2C8 can only be <7>
R2C3 can only be <9>
R8C2 can only be <7>
R2C2 can only be <5>
R9C3 can only be <3>
R3C1 can only be <8>
R3C3 can only be <6>
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