Aug 21 - Very Hard
Puzzle Copyright © Kevin Stone
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Reasoning
R8C7 can only be <8>
R4C8 is the only square in row 4 that can be <8>
R5C8 is the only square in row 5 that can be <4>
R3C9 is the only square in row 3 that can be <4>
R8C5 is the only square in row 8 that can be <4>
R9C1 is the only square in row 9 that can be <4>
Intersection of row 2 with block 1. The value <5> only appears in one or more of squares R2C1, R2C2 and R2C3 of row 2. These squares are the ones that intersect with block 1. Thus, the other (non-intersecting) squares of block 1 cannot contain this value.
R1C1 - removing <5> from <256> leaving <26>
R1C3 - removing <5> from <5689> leaving <689>
Squares R2C5 and R2C7 in row 2 and R5C5 and R5C7 in row 5 form a Simple X-Wing pattern on possibility <3>. All other instances of this possibility in columns 5 and 7 can be removed.
R1C5 - removing <3> from <3679> leaving <679>
R1C7 - removing <3> from <239> leaving <29>
R6C5 - removing <3> from <12369> leaving <1269>
R6C7 - removing <3> from <1236> leaving <126>
R9C7 - removing <3> from <36> leaving <6>
R4C9 is the only square in column 9 that can be <6>
R3C6 is the only square in column 6 that can be <6>
R7C9 is the only square in column 9 that can be <1>
Squares R3C1 and R3C8 in row 3 form a simple naked pair. These 2 squares both contain the 2 possibilities <12>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the row.
R3C2 - removing <2> from <289> leaving <89>
Intersection of column 2 with block 4. The value <2> only appears in one or more of squares R4C2, R5C2 and R6C2 of column 2. These squares are the ones that intersect with block 4. Thus, the other (non-intersecting) squares of block 4 cannot contain this value.
R6C1 - removing <2> from <1256> leaving <156>
Squares R3C1 and R6C1 in column 1 and R3C8 and R6C8 in column 8 form a Simple X-Wing pattern on possibility <1>. All other instances of this possibility in rows 3 and 6 can be removed.
R6C5 - removing <1> from <1269> leaving <269>
R6C7 - removing <1> from <12> leaving <2>
R1C7 can only be <9>
R1C5 can only be <7>
R9C5 can only be <2>
R9C6 can only be <5>
R9C9 can only be <3>
R7C6 can only be <9>
R1C9 can only be <5>
R7C4 can only be <7>
R4C6 can only be <2>
R7C8 can only be <5>
R7C1 can only be <6>
R8C8 can only be <7>
R8C3 can only be <5>
R7C2 can only be <3>
R1C1 can only be <2>
R1C8 can only be <3>
R3C1 can only be <1>
R1C4 can only be <8>
R6C8 can only be <1>
R2C7 can only be <1>
R2C3 can only be <9>
R5C7 can only be <3>
R3C8 can only be <2>
R6C1 can only be <5>
R1C3 can only be <6>
R3C4 can only be <9>
R2C2 can only be <5>
R2C5 can only be <3>
R3C2 can only be <8>
R9C2 can only be <7>
R6C4 can only be <3>
R9C3 can only be <8>
R4C2 can only be <9>
R5C3 can only be <1>
R4C5 can only be <1>
R6C2 can only be <6>
R4C3 can only be <7>
R5C5 can only be <6>
R5C2 can only be <2>
R6C5 can only be <9>
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