Feb 12 - Very Hard
Puzzle Copyright © Kevin Stone
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Reasoning
R3C3 is the only square in row 3 that can be <8>
R3C1 is the only square in row 3 that can be <5>
R5C7 is the only square in row 5 that can be <8>
R9C7 is the only square in row 9 that can be <6>
R1C3 is the only square in row 1 that can be <6>
R2C1 is the only square in column 1 that can be <3>
R2C2 is the only square in row 2 that can be <7>
R1C2 can only be <1>
R6C2 can only be <5>
R1C5 is the only square in row 1 that can be <7>
R5C5 is the only square in row 5 that can be <5>
R8C4 is the only square in row 8 that can be <5>
R9C3 is the only square in row 9 that can be <5>
R9C5 is the only square in row 9 that can be <4>
R3C4 is the only square in column 4 that can be <9>
Squares R1C7 and R1C8 in block 3 form a simple naked pair. These 2 squares both contain the 2 possibilities <39>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the block.
R3C7 - removing <3> from <123> leaving <12>
Intersection of row 7 with block 8. The values <38> 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 these values.
R8C6 - removing <8> from <128> leaving <12>
Intersection of column 1 with block 7. The value <7> only appears in one or more of squares R7C1, R8C1 and R9C1 of column 1. These squares are the ones that intersect with block 7. Thus, the other (non-intersecting) squares of block 7 cannot contain this value.
R7C3 - removing <7> from <247> leaving <24>
Intersection of column 9 with block 9. The value <7> only appears in one or more of squares R7C9, R8C9 and R9C9 of column 9. 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 <7> from <1279> leaving <129>
Squares R3C5 and R7C5 in column 5 and R3C7 and R7C7 in column 7 form a Simple X-Wing pattern on possibility <2>. All other instances of this possibility in rows 3 and 7 can be removed.
R7C3 - removing <2> from <24> leaving <4>
R3C6 - removing <2> from <1236> leaving <136>
R7C6 - removing <2> from <1238> leaving <138>
R5C3 can only be <1>
R6C3 can only be <7>
R4C3 can only be <2>
R4C2 can only be <9>
R5C1 can only be <4>
R5C9 can only be <9>
R4C7 is the only square in row 4 that can be <7>
R2C9 is the only square in column 9 that can be <4>
R3C9 is the only square in column 9 that can be <6>
Squares R7C9 and R8C9 in block 9 form a simple naked pair. These 2 squares both contain the 2 possibilities <17>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the block.
R7C7 - removing <1> from <129> leaving <29>
R8C8 - removing <1> from <1289> leaving <289>
Squares R9C2, R9C8, R8C2 and R8C8 form a Type-1 Unique Rectangle on <28>.
R8C8 - removing <28> from <289> leaving <9>
R8C1 can only be <7>
R1C8 can only be <3>
R7C7 can only be <2>
R1C7 can only be <9>
R4C8 can only be <4>
R6C8 can only be <1>
R6C7 can only be <3>
R2C8 can only be <2>
R7C5 can only be <3>
R3C7 can only be <1>
R9C8 can only be <8>
R8C9 can only be <1>
R7C1 can only be <9>
R8C6 can only be <2>
R7C9 can only be <7>
R9C2 can only be <2>
R3C6 can only be <3>
R6C4 can only be <8>
R3C5 can only be <2>
R8C2 can only be <8>
R4C6 can only be <6>
R4C4 can only be <3>
R2C6 can only be <1>
R6C6 can only be <4>
R7C4 can only be <1>
R7C6 can only be <8>
R2C4 can only be <6>
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