Jan 16 - Very Hard
Puzzle Copyright © Kevin Stone
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Reasoning
R3C5 can only be <8>
R5C5 can only be <4>
R7C5 can only be <5>
R4C6 is the only square in row 4 that can be <9>
R4C4 is the only square in row 4 that can be <3>
R6C3 is the only square in row 6 that can be <5>
R8C9 is the only square in row 8 that can be <5>
R9C2 is the only square in row 9 that can be <5>
Squares R6C4 and R6C6 in row 6 form a simple naked pair. These 2 squares both contain the 2 possibilities <78>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the row.
R6C1 - removing <7> from <267> leaving <26>
R6C7 - removing <8> from <468> leaving <46>
R6C9 - removing <8> from <2468> leaving <246>
Intersection of column 8 with block 3. The value <2> only appears in one or more of squares R1C8, R2C8 and R3C8 of column 8. These squares are the ones that intersect with block 3. Thus, the other (non-intersecting) squares of block 3 cannot contain this value.
R2C9 - removing <2> from <289> leaving <89>
R3C9 - removing <2> from <269> leaving <69>
Intersection of row 2 with block 1. The value <2> 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.
R1C3 - removing <2> from <2678> leaving <678>
R3C1 - removing <2> from <2367> leaving <367>
Intersection of column 8 with block 9. The value <1> only appears in one or more of squares R7C8, R8C8 and R9C8 of column 8. These squares are the ones that intersect with block 9. Thus, the other (non-intersecting) squares of block 9 cannot contain this value.
R8C7 - removing <1> from <147> leaving <47>
R9C7 - removing <1> from <14679> leaving <4679>
Intersection of row 8 with block 7. The value <1> 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.
R7C1 - removing <1> from <1467> leaving <467>
R9C3 - removing <1> from <1679> leaving <679>
Squares R3C2 and R3C9 in row 3 and R7C2 and R7C9 in row 7 form a Simple X-Wing pattern on possibility <9>. All other instances of this possibility in columns 2 and 9 can be removed.
R2C9 - removing <9> from <89> leaving <8>
R4C9 can only be <2>
R1C3 is the only square in row 1 that can be <8>
R4C7 is the only square in row 4 that can be <8>
R6C1 is the only square in row 6 that can be <2>
R2C1 can only be <3>
R2C7 can only be <9>
R2C3 can only be <2>
R3C9 can only be <6>
R3C1 can only be <7>
R6C9 can only be <4>
R6C7 can only be <6>
R7C9 can only be <9>
R3C2 can only be <9>
R3C8 can only be <2>
R4C1 can only be <1>
R1C2 can only be <6>
R3C4 can only be <1>
R1C8 can only be <7>
R4C3 can only be <7>
R8C1 can only be <4>
R5C3 can only be <6>
R8C3 can only be <1>
R5C7 can only be <1>
R9C3 can only be <9>
R8C7 can only be <7>
R7C1 can only be <6>
R1C7 can only be <3>
R9C7 can only be <4>
R7C2 can only be <7>
R1C6 can only be <4>
R3C6 can only be <3>
R9C4 can only be <7>
R7C8 can only be <1>
R9C8 can only be <6>
R9C6 can only be <1>
R6C4 can only be <8>
R1C4 can only be <2>
R7C6 can only be <8>
R6C6 can only be <7>
R7C4 can only be <4>
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