Sep 09 - Very Hard
Puzzle Copyright © Kevin Stone
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Reasoning
R5C5 can only be <1>
R9C6 can only be <8>
R3C1 is the only square in row 3 that can be <7>
R5C9 is the only square in row 5 that can be <3>
R5C8 is the only square in row 5 that can be <7>
R9C7 is the only square in row 9 that can be <7>
Squares R5C1 and R5C2 in block 4 form a simple naked pair. These 2 squares both contain the 2 possibilities <69>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the block.
R6C1 - removing <6> from <468> leaving <48>
Intersection of row 2 with block 3. The value <1> only appears in one or more of squares R2C7, R2C8 and R2C9 of row 2. 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 <1> from <1469> leaving <469>
R1C8 - removing <1> from <1468> leaving <468>
Intersection of row 8 with block 9. The value <1> only appears in one or more of squares R8C7, R8C8 and R8C9 of row 8. These squares are the ones that intersect with block 9. Thus, the other (non-intersecting) squares of block 9 cannot contain this value.
R7C7 - removing <1> from <169> leaving <69>
R7C9 - removing <1> from <1689> leaving <689>
Intersection of row 9 with block 7. The value <9> only appears in one or more of squares R9C1, R9C2 and R9C3 of row 9. These squares are the ones that intersect with block 7. Thus, the other (non-intersecting) squares of block 7 cannot contain this value.
R7C1 - removing <9> from <23689> leaving <2368>
R7C3 - removing <9> from <2389> leaving <238>
Intersection of column 1 with block 4. The value <4> only appears in one or more of squares R4C1, R5C1 and R6C1 of column 1. These squares are the ones that intersect with block 4. Thus, the other (non-intersecting) squares of block 4 cannot contain this value.
R4C3 - removing <4> from <124> leaving <12>
R6C3 - removing <4> from <148> leaving <18>
Intersection of column 7 with block 6. The value <1> only appears in one or more of squares R4C7, R5C7 and R6C7 of column 7. These squares are the ones that intersect with block 6. Thus, the other (non-intersecting) squares of block 6 cannot contain this value.
R4C9 - removing <1> from <145> leaving <45>
R6C9 - removing <1> from <146> leaving <46>
Squares R4C1<24>, R6C1<48> and R8C1<28> in column 1 form a comprehensive naked triplet. These 3 squares can only contain the 3 possibilities <248>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the column.
R2C1 - removing <8> from <389> leaving <39>
R7C1 - removing <28> from <2368> leaving <36>
Squares R3C3 and R3C6 in row 3 and R7C3 and R7C6 in row 7 form a Simple X-Wing pattern on possibility <2>. All other instances of this possibility in columns 3 and 6 can be removed.
R1C3 - removing <2> from <23489> leaving <3489>
R1C6 - removing <2> from <126> leaving <16>
R4C3 - removing <2> from <12> leaving <1>
R6C3 can only be <8>
R6C1 can only be <4>
R6C9 can only be <6>
R4C1 can only be <2>
R6C7 can only be <1>
R8C1 can only be <8>
R7C9 is the only square in row 7 that can be <8>
R7C7 is the only square in row 7 that can be <9>
R7C1 is the only square in row 7 that can be <6>
R5C1 can only be <9>
R5C2 can only be <6>
R2C1 can only be <3>
R2C5 can only be <5>
R3C4 can only be <9>
R8C2 is the only square in row 8 that can be <5>
R9C2 can only be <9>
R9C3 can only be <3>
R2C2 can only be <8>
R9C4 can only be <5>
R9C5 can only be <4>
R7C3 can only be <2>
R9C8 can only be <6>
R8C5 can only be <2>
R2C8 can only be <1>
R1C2 can only be <2>
R2C9 can only be <9>
R8C8 can only be <4>
R7C6 can only be <1>
R3C3 can only be <4>
R7C4 can only be <3>
R1C6 can only be <6>
R1C5 can only be <3>
R8C9 can only be <1>
R1C8 can only be <8>
R1C4 can only be <1>
R1C7 can only be <4>
R3C6 can only be <2>
R1C3 can only be <9>
R4C7 can only be <5>
R3C9 can only be <5>
R3C7 can only be <6>
R4C9 can only be <4>
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