Oct 09 - Very Hard
Puzzle Copyright © Kevin Stone
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Reasoning
R2C3 can only be <9>
R5C2 is the only square in column 2 that can be <4>
R6C9 is the only square in column 9 that can be <7>
Intersection of row 5 with block 5. The values <37> only appears in one or more of squares R5C4, R5C5 and R5C6 of row 5. These squares are the ones that intersect with block 5. Thus, the other (non-intersecting) squares of block 5 cannot contain these values.
R6C5 - removing <3> from <138> leaving <18>
R6C6 - removing <3> from <12389> leaving <1289>
Intersection of column 2 with block 7. The value <1> only appears in one or more of squares R7C2, R8C2 and R9C2 of column 2. These squares are the ones that intersect with block 7. Thus, the other (non-intersecting) squares of block 7 cannot contain this value.
R8C3 - removing <1> from <1357> leaving <357>
R9C3 - removing <1> from <1235> leaving <235>
Squares R2C9<48>, R3C9<58> and R8C9<45> in column 9 form a comprehensive naked triplet. These 3 squares can only contain the 3 possibilities <458>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the column.
R4C9 - removing <8> from <289> leaving <29>
R7C9 - removing <4> from <249> leaving <29>
Intersection of row 7 with block 8. The value <4> only appears in one or more of squares R7C4, R7C5 and R7C6 of row 7. These squares are the ones that intersect with block 8. Thus, the other (non-intersecting) squares of block 8 cannot contain this value.
R8C5 - removing <4> from <134> leaving <13>
Intersection of column 9 with block 3. The value <8> only appears in one or more of squares R1C9, R2C9 and R3C9 of column 9. These squares are the ones that intersect with block 3. Thus, the other (non-intersecting) squares of block 3 cannot contain this value.
R1C7 - removing <8> from <4689> leaving <469>
R2C7 - removing <8> from <1468> leaving <146>
Squares R2C5 and R2C7 in row 2 and R8C5 and R8C7 in row 8 form a Simple X-Wing pattern on possibility <1>. All other instances of this possibility in columns 5 and 7 can be removed.
R4C5 - removing <1> from <1468> leaving <468>
R6C5 - removing <1> from <18> leaving <8>
R9C7 - removing <1> from <139> leaving <39>
R6C7 can only be <9>
R9C7 can only be <3>
R4C9 can only be <2>
R4C1 can only be <5>
R7C9 can only be <9>
R5C8 can only be <6>
R5C4 can only be <7>
R5C5 can only be <3>
R4C7 can only be <8>
R4C3 can only be <1>
R5C6 can only be <2>
R8C5 can only be <1>
R6C6 can only be <1>
R6C4 can only be <5>
R8C7 can only be <4>
R8C9 can only be <5>
R1C7 can only be <6>
R3C9 can only be <8>
R2C7 can only be <1>
R3C8 can only be <5>
R1C8 can only be <9>
R3C2 can only be <3>
R3C6 can only be <7>
R2C9 can only be <4>
R2C5 can only be <6>
R3C1 can only be <6>
R2C1 can only be <8>
R4C5 can only be <4>
R3C4 can only be <1>
R4C6 can only be <9>
R4C4 can only be <6>
R9C6 can only be <8>
R9C4 can only be <9>
R1C6 can only be <4>
R7C4 can only be <4>
R1C4 can only be <8>
R7C6 can only be <3>
R1C2 can only be <5>
R7C1 can only be <2>
R1C3 can only be <7>
R9C2 can only be <1>
R8C3 can only be <3>
R7C8 can only be <1>
R6C1 can only be <3>
R9C3 can only be <5>
R7C2 can only be <8>
R9C8 can only be <2>
R8C1 can only be <7>
R6C3 can only be <2>
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