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Jan 25 - Very Hard
Puzzle Copyright © Kevin Stone
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Reasoning
R2C3 can only be <5>
R2C7 can only be <4>
R5C8 can only be <4>
R1C3 is the only square in row 1 that can be <6>
R2C8 is the only square in row 2 that can be <9>
R7C1 is the only square in row 7 that can be <4>
R7C2 is the only square in row 7 that can be <7>
R7C9 is the only square in row 7 that can be <2>
R8C7 can only be <3>
R9C7 can only be <1>
R5C7 can only be <7>
R1C7 can only be <2>
R1C9 is the only square in row 1 that can be <7>
R1C6 is the only square in row 1 that can be <5>
R5C5 is the only square in row 5 that can be <5>
R6C5 is the only square in row 6 that can be <7>
R9C9 is the only square in row 9 that can be <5>
R3C9 can only be <8>
R3C8 can only be <5>
Squares R6C6 and R6C9 in row 6 form a simple naked pair. These 2 squares both contain the 2 possibilities <16>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the row.
R6C1 - removing <1> from <129> leaving <29>
Intersection of column 3 with block 7. The value <9> only appears in one or more of squares R7C3, R8C3 and R9C3 of column 3. These squares are the ones that intersect with block 7. Thus, the other (non-intersecting) squares of block 7 cannot contain this value.
R9C1 - removing <9> from <389> leaving <38>
Squares R1C1 and R9C1 in column 1 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.
R3C1 - removing <3> from <123> leaving <12>
R4C1 - removing <3> from <139> leaving <19>
Intersection of row 4 with block 5. The values <34> only appears in one or more of squares R4C4, R4C5 and R4C6 of row 4. These squares are the ones that intersect with block 5. Thus, the other (non-intersecting) squares of block 5 cannot contain these values.
R5C4 - removing <3> from <238> leaving <28>
Intersection of column 6 with block 5. The values <16> only appears in one or more of squares R4C6, R5C6 and R6C6 of column 6. These squares are the ones that intersect with block 5. Thus, the other (non-intersecting) squares of block 5 cannot contain these values.
R4C5 - removing <16> from <1369> leaving <39>
Squares R6C6, R6C9, R4C6 and R4C9 form a Type-1 Unique Rectangle on <16>.
R4C6 - removing <16> from <146> leaving <4>
R9C6 can only be <8>
R9C1 can only be <3>
R5C6 can only be <1>
R7C5 can only be <6>
R6C6 can only be <6>
R6C9 can only be <1>
R4C9 can only be <6>
R7C8 can only be <8>
R8C5 can only be <9>
R8C8 can only be <6>
R8C3 can only be <2>
R4C5 can only be <3>
R9C4 can only be <4>
R9C3 can only be <9>
R1C1 can only be <8>
R1C4 can only be <3>
R2C2 can only be <1>
R4C4 can only be <9>
R3C5 can only be <1>
R2C5 can only be <8>
R3C1 can only be <2>
R3C2 can only be <3>
R6C1 can only be <9>
R5C2 can only be <2>
R4C1 can only be <1>
R6C4 can only be <2>
R5C3 can only be <3>
R5C4 can only be <8>
R8C2 can only be <8>
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