Feb 16 - Very Hard
Puzzle Copyright © Kevin Stone
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Reasoning
R1C9 is the only square in row 1 that can be <5>
R5C5 is the only square in column 5 that can be <2>
R2C5 is the only square in column 5 that can be <6>
R1C5 is the only square in block 2 that can be <8>
R8C5 can only be <5>
R9C8 is the only square in row 9 that can be <5>
R5C6 is the only square in column 6 that can be <5>
R2C9 is the only square in block 3 that can be <3>
R9C9 can only be <1>
R9C5 can only be <7>
R7C5 can only be <1>
Squares R3C7 and R6C7 in column 7 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 column.
R7C7 - removing <2> from <234> leaving <34>
Intersection of row 1 with block 1. The values <347> only appears in one or more of squares R1C1, R1C2 and R1C3 of row 1. These squares are the ones that intersect with block 1. Thus, the other (non-intersecting) squares of block 1 cannot contain these values.
R2C1 - removing <4> from <49> leaving <9>
R2C2 - removing <47> from <1247> leaving <12>
R3C2 - removing <7> from <12678> leaving <1268>
R3C3 - removing <7> from <12679> leaving <1269>
R3C6 is the only square in row 3 that can be <9>
R3C8 is the only square in row 3 that can be <7>
R6C3 is the only square in row 6 that can be <9>
Squares R7C6 and R7C7 in row 7 form a simple naked pair. These 2 squares both contain the 2 possibilities <34>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the row.
R7C1 - removing <34> from <3456> leaving <56>
R7C2 - removing <34> from <34567> leaving <567>
R7C3 - removing <34> from <3467> leaving <67>
R7C4 - removing <34> from <3489> leaving <89>
R1C1 is the only square in column 1 that can be <4>
R4C1 is the only square in column 1 that can be <3>
R4C6 can only be <7>
R2C6 can only be <4>
R2C4 can only be <7>
R7C6 can only be <3>
R7C7 can only be <4>
R9C4 can only be <4>
R9C7 can only be <3>
R5C4 is the only square in row 5 that can be <3>
R6C9 is the only square in row 6 that can be <7>
R3C1 is the only square in column 1 that can be <8>
Squares R8C4<89>, R8C8<68> and R8C9<689> in row 8 form a comprehensive naked triplet. These 3 squares can only contain the 3 possibilities <689>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the row.
R8C2 - removing <6> from <346> leaving <34>
R8C3 - removing <6> from <346> leaving <34>
Intersection of row 8 with block 9. The value <6> 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.
R7C8 - removing <6> from <268> leaving <28>
R7C9 - removing <6> from <2689> leaving <289>
Squares R2C2 and R6C7 form a remote naked pair. <12> can be removed from any square that is common to their groups.
R6C2 - removing <12> from <1256> leaving <56>
R6C7 is the only square in row 6 that can be <2>
R3C7 can only be <1>
R2C8 can only be <2>
R2C2 can only be <1>
R7C8 can only be <8>
R7C4 can only be <9>
R8C8 can only be <6>
R8C9 can only be <9>
R5C8 can only be <1>
R8C4 can only be <8>
R7C9 can only be <2>
R6C4 is the only square in row 6 that can be <1>
R4C4 can only be <6>
R4C9 can only be <8>
R4C2 can only be <2>
R5C9 can only be <6>
R5C3 can only be <4>
R4C3 can only be <1>
R3C2 can only be <6>
R5C2 can only be <8>
R8C3 can only be <3>
R8C2 can only be <4>
R1C3 can only be <7>
R1C2 can only be <3>
R7C3 can only be <6>
R3C3 can only be <2>
R6C2 can only be <5>
R6C1 can only be <6>
R7C2 can only be <7>
R7C1 can only be <5>
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