Aug 31 - Very Hard
Puzzle Copyright © Kevin Stone
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Reasoning
R5C5 can only be <8>
R5C2 can only be <2>
R2C6 is the only square in row 2 that can be <5>
R3C6 can only be <3>
R3C2 is the only square in row 3 that can be <5>
R6C8 is the only square in row 6 that can be <5>
R6C2 is the only square in row 6 that can be <6>
R8C9 is the only square in row 8 that can be <5>
R5C1 is the only square in column 1 that can be <3>
R2C1 is the only square in column 1 that can be <4>
R4C3 is the only square in column 3 that can be <4>
R3C7 is the only square in column 7 that can be <4>
R2C7 is the only square in column 7 that can be <9>
R1C9 is the only square in column 9 that can be <3>
R2C4 is the only square in block 2 that can be <8>
Intersection of column 7 with block 9. The value <2> only appears in one or more of squares R7C7, R8C7 and R9C7 of column 7. These squares are the ones that intersect with block 9. Thus, the other (non-intersecting) squares of block 9 cannot contain this value.
R7C8 - removing <2> from <2368> leaving <368>
Squares R9C1<68>, R9C8<468> and R9C9<46> in row 9 form a comprehensive naked triplet. These 3 squares can only contain the 3 possibilities <468>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the row.
R9C2 - removing <8> from <789> leaving <79>
R9C5 - removing <6> from <679> leaving <79>
Squares R3C4 and R3C8 in row 3 and R7C4 and R7C8 in row 7 form a Simple X-Wing pattern on possibility <6>. All other instances of this possibility in columns 4 and 8 can be removed.
R8C4 - removing <6> from <36> leaving <3>
R9C8 - removing <6> from <468> leaving <48>
Squares R1C2 and R1C5 in row 1 and R9C2 and R9C5 in row 9 form a Simple X-Wing pattern on possibility <9>. All other instances of this possibility in columns 2 and 5 can be removed.
R7C2 - removing <9> from <189> leaving <18>
Squares R7C2 and R7C6 in row 7 form a simple naked pair. These 2 squares both contain the 2 possibilities <18>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the row.
R7C3 - removing <18> from <1289> leaving <29>
R7C7 - removing <8> from <238> leaving <23>
R7C8 - removing <8> from <368> leaving <36>
Squares R3C3 and R7C3 in column 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 column.
R2C3 - removing <2> from <12> leaving <1>
R8C3 - removing <2> from <1278> leaving <178>
R2C9 can only be <6>
R2C5 can only be <2>
R9C9 can only be <4>
R3C8 can only be <2>
R3C3 can only be <9>
R1C8 can only be <1>
R9C8 can only be <8>
R5C9 can only be <1>
R5C8 can only be <4>
R1C5 can only be <9>
R3C4 can only be <6>
R7C3 can only be <2>
R1C2 can only be <8>
R7C4 can only be <9>
R7C7 can only be <3>
R9C5 can only be <7>
R7C8 can only be <6>
R9C2 can only be <9>
R8C5 can only be <6>
R9C1 can only be <6>
R4C8 can only be <3>
R8C7 can only be <2>
R1C1 can only be <2>
R4C2 can only be <7>
R7C2 can only be <1>
R4C7 can only be <8>
R6C3 can only be <8>
R6C7 can only be <7>
R8C3 can only be <7>
R7C6 can only be <8>
R8C6 can only be <1>
R8C1 can only be <8>
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