Sep 27 - Very Hard
Puzzle Copyright © Kevin Stone
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Reasoning
R1C7 can only be <7>
R5C7 can only be <3>
R5C9 can only be <7>
R2C7 can only be <1>
R7C9 can only be <3>
R9C9 can only be <2>
R1C9 can only be <9>
R3C9 can only be <8>
R9C7 can only be <4>
R8C7 can only be <5>
R8C8 can only be <1>
R7C8 can only be <7>
R5C6 is the only square in row 5 that can be <9>
R7C2 is the only square in row 7 that can be <9>
R9C1 is the only square in column 1 that can be <3>
Squares R2C6 and R2C8 in row 2 form a simple naked pair. These 2 squares both contain the 2 possibilities <23>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the row.
R2C2 - removing <2> from <258> leaving <58>
R2C3 - removing <2> from <268> leaving <68>
R2C4 - removing <3> from <356> leaving <56>
Squares R4C4 and R4C8 in row 4 form a simple naked pair. These 2 squares both contain the 2 possibilities <46>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the row.
R4C5 - removing <46> from <2468> leaving <28>
Intersection of column 4 with block 5. The value <1> only appears in one or more of squares R4C4, R5C4 and R6C4 of column 4. These squares are the ones that intersect with block 5. Thus, the other (non-intersecting) squares of block 5 cannot contain this value.
R5C5 - removing <1> from <1256> leaving <256>
R6C5 - removing <1> from <1346> leaving <346>
Intersection of block 4 with row 5. The value <6> only appears in one or more of squares R5C1, R5C2 and R5C3 of block 4. These squares are the ones that intersect with row 5. Thus, the other (non-intersecting) squares of row 5 cannot contain this value.
R5C4 - removing <6> from <156> leaving <15>
R5C5 - removing <6> from <256> leaving <25>
Squares R4C4, R4C8, R6C4 and R6C8 form a Type-1 Unique Rectangle on <46>.
R6C4 - removing <46> from <1346> leaving <13>
Squares R6C2<17>, R6C4<13> and R6C6<37> in row 6 form a comprehensive naked triplet. These 3 squares can only contain the 3 possibilities <137>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the row.
R6C5 - removing <3> from <346> leaving <46>
R3C5 is the only square in column 5 that can be <3>
R3C8 can only be <2>
R2C6 can only be <2>
R3C1 can only be <1>
R2C8 can only be <3>
R1C5 can only be <6>
R3C2 can only be <5>
R7C1 can only be <4>
R2C2 can only be <8>
R7C5 can only be <1>
R9C5 can only be <8>
R9C3 can only be <1>
R4C5 can only be <2>
R8C6 can only be <3>
R1C1 can only be <2>
R6C5 can only be <4>
R2C4 can only be <5>
R2C3 can only be <6>
R8C2 can only be <2>
R5C4 can only be <1>
R4C2 can only be <7>
R5C5 can only be <5>
R5C3 can only be <2>
R6C4 can only be <3>
R6C6 can only be <7>
R8C4 can only be <4>
R6C8 can only be <6>
R4C4 can only be <6>
R6C2 can only be <1>
R4C6 can only be <8>
R4C8 can only be <4>
R8C3 can only be <8>
R1C3 can only be <4>
R5C1 can only be <6>
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