Aug 23 - Very Hard
Puzzle Copyright © Kevin Stone
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Reasoning
R1C7 can only be <4>
R5C5 can only be <5>
R9C3 can only be <3>
R9C7 can only be <1>
R8C2 can only be <5>
R9C4 can only be <9>
R7C1 can only be <9>
R7C5 can only be <6>
R1C5 can only be <1>
R8C5 can only be <3>
R1C4 is the only square in row 1 that can be <6>
R2C5 is the only square in row 2 that can be <9>
R8C4 is the only square in row 8 that can be <1>
Squares R2C2 and R6C2 in column 2 form a simple naked pair. These 2 squares both contain the 2 possibilities <38>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the column.
R5C2 - removing <38> from <3489> leaving <49>
Intersection of column 7 with block 6. The values <235> 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 these values.
R4C8 - removing <2> from <2467> leaving <467>
R4C9 - removing <2> from <279> leaving <79>
R5C8 - removing <2> from <248> leaving <48>
R5C9 - removing <2> from <1289> leaving <189>
Squares R1C6<58>, R2C4<28> and R3C4<25> in block 2 form a comprehensive naked triplet. These 3 squares can only contain the 3 possibilities <258>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the block.
R2C6 - removing <28> from <2378> leaving <37>
R3C6 - removing <25> from <23457> leaving <347>
Intersection of column 6 with block 8. The value <2> only appears in one or more of squares R7C6, R8C6 and R9C6 of column 6. These squares are the ones that intersect with block 8. Thus, the other (non-intersecting) squares of block 8 cannot contain this value.
R7C4 - removing <2> from <258> leaving <58>
Squares R9C5, R9C6, R3C5 and R3C6 form a Type-1 Unique Rectangle on <47>.
R3C6 - removing <47> from <347> leaving <3>
R3C1 can only be <5>
R2C6 can only be <7>
R2C8 can only be <2>
R9C6 can only be <4>
R3C5 can only be <4>
R2C4 can only be <8>
R8C8 can only be <8>
R3C9 can only be <7>
R3C4 can only be <2>
R4C1 can only be <6>
R1C3 can only be <8>
R9C5 can only be <7>
R4C9 can only be <9>
R4C2 can only be <4>
R8C6 can only be <2>
R5C8 can only be <4>
R7C9 can only be <2>
R1C6 can only be <5>
R5C3 can only be <2>
R2C2 can only be <3>
R6C2 can only be <8>
R7C4 can only be <5>
R4C8 can only be <7>
R5C2 can only be <9>
R6C8 can only be <6>
R5C7 can only be <3>
R4C3 can only be <5>
R5C1 can only be <1>
R6C7 can only be <5>
R6C9 can only be <1>
R6C3 can only be <7>
R4C7 can only be <2>
R6C1 can only be <3>
R5C9 can only be <8>
R7C6 can only be <8>
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