Jun 07 - Very Hard
Puzzle Copyright © Kevin Stone
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Reasoning
R8C8 can only be <6>
R3C3 is the only square in row 3 that can be <7>
R4C6 is the only square in row 4 that can be <7>
R7C3 is the only square in row 7 that can be <6>
R3C7 is the only square in column 7 that can be <6>
R2C7 is the only square in column 7 that can be <4>
R7C7 is the only square in column 7 that can be <2>
R9C1 is the only square in row 9 that can be <2>
R8C7 is the only square in column 7 that can be <3>
R9C9 can only be <5>
R9C6 can only be <1>
R7C9 can only be <8>
R7C8 can only be <1>
R9C4 can only be <3>
Intersection of row 8 with block 7. The value <9> only appears in one or more of squares R8C1, R8C2 and R8C3 of row 8. These squares are the ones that intersect with block 7. Thus, the other (non-intersecting) squares of block 7 cannot contain this value.
R7C2 - removing <9> from <349> leaving <34>
Intersection of column 2 with block 1. The value <2> only appears in one or more of squares R1C2, R2C2 and R3C2 of column 2. These squares are the ones that intersect with block 1. Thus, the other (non-intersecting) squares of block 1 cannot contain this value.
R2C3 - removing <2> from <259> leaving <59>
Squares R5C3<12>, R5C5<25> and R5C7<15> in row 5 form a comprehensive naked triplet. These 3 squares can only contain the 3 possibilities <125>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the row.
R5C4 - removing <125> from <12569> leaving <69>
R5C6 - removing <5> from <569> leaving <69>
Squares R2C3 and R2C5 in row 2 and R8C3 and R8C5 in row 8 form a Simple X-Wing pattern on possibility <5>. All other instances of this possibility in columns 3 and 5 can be removed.
R4C5 - removing <5> from <358> leaving <38>
R5C5 - removing <5> from <25> leaving <2>
R5C3 can only be <1>
R5C7 can only be <5>
R4C3 can only be <3>
R4C5 can only be <8>
R6C3 can only be <2>
R4C7 can only be <1>
R2C5 can only be <5>
R6C6 can only be <4>
R4C4 can only be <5>
R6C7 can only be <8>
R6C4 can only be <1>
R6C5 can only be <3>
R2C3 can only be <9>
R8C5 can only be <4>
R3C6 can only be <8>
R3C8 can only be <9>
R1C6 can only be <6>
R2C8 can only be <8>
R8C2 can only be <9>
R7C4 can only be <9>
R1C4 can only be <2>
R5C6 can only be <9>
R2C2 can only be <2>
R8C3 can only be <5>
R5C4 can only be <6>
R7C6 can only be <5>
R7C1 can only be <3>
R1C9 can only be <3>
R3C4 can only be <4>
R1C1 can only be <8>
R3C9 can only be <2>
R3C2 can only be <3>
R3C1 can only be <5>
R7C2 can only be <4>
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