Jun 29 - Very Hard
Puzzle Copyright © Kevin Stone
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Reasoning
R2C1 can only be <2>
R2C2 can only be <4>
R3C7 can only be <3>
R7C3 can only be <3>
R3C3 can only be <9>
R3C4 is the only square in row 3 that can be <4>
R4C9 is the only square in row 4 that can be <2>
R9C9 is the only square in row 9 that can be <9>
R9C8 is the only square in row 9 that can be <4>
R1C8 is the only square in column 8 that can be <2>
R8C9 is the only square in column 9 that can be <3>
R8C8 is the only square in row 8 that can be <5>
R2C8 can only be <8>
R7C7 can only be <6>
R2C5 can only be <7>
R5C8 can only be <6>
R2C9 can only be <5>
R1C9 can only be <7>
R8C2 is the only square in row 8 that can be <7>
R9C4 is the only square in row 9 that can be <7>
Squares R3C5 and R7C5 in column 5 form a simple naked pair. These 2 squares both contain the 2 possibilities <28>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the column.
R5C5 - removing <8> from <1389> leaving <139>
R9C5 - removing <8> from <1368> leaving <136>
Intersection of row 7 with block 8. The values <258> 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.
R9C6 - removing <8> from <368> leaving <36>
Intersection of column 3 with block 4. The values <147> only appears in one or more of squares R4C3, R5C3 and R6C3 of column 3. These squares are the ones that intersect with block 4. Thus, the other (non-intersecting) squares of block 4 cannot contain these values.
R4C1 - removing <1> from <1358> leaving <358>
R5C1 - removing <1> from <13589> leaving <3589>
R5C2 - removing <1> from <138> leaving <38>
R6C1 - removing <1> from <189> leaving <89>
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 <139> leaving <39>
Squares R3C5, R3C6, R7C5 and R7C6 form a Type-1 Unique Rectangle on <28>.
R7C6 - removing <28> from <258> leaving <5>
R7C4 can only be <8>
R7C5 can only be <2>
R4C4 can only be <1>
R3C5 can only be <8>
R3C6 can only be <2>
R4C3 can only be <7>
R6C4 can only be <6>
R1C4 can only be <5>
R4C7 can only be <5>
R5C7 can only be <1>
R5C3 can only be <4>
R6C7 can only be <7>
R5C9 can only be <8>
R6C3 can only be <1>
R5C2 can only be <3>
R6C9 can only be <4>
R5C5 can only be <9>
R1C2 can only be <1>
R4C1 can only be <8>
R5C1 can only be <5>
R1C5 can only be <6>
R6C6 can only be <8>
R6C1 can only be <9>
R4C6 can only be <3>
R1C1 can only be <3>
R9C2 can only be <8>
R1C6 can only be <9>
R8C5 can only be <1>
R9C6 can only be <6>
R8C1 can only be <6>
R9C5 can only be <3>
R9C1 can only be <1>
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