Feb 07 - Hard

Puzzle Copyright © Kevin Stone

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## Reasoning

R7C2 is the only square in row 7 that can be <4>

R3C7 is the only square in column 7 that can be <6>

R3C3 can only be <5>

R7C8 is the only square in row 7 that can be <5>

R2C9 is the only square in row 2 that can be <5>

R7C3 is the only square in row 7 that can be <8>

R2C3 can only be <7>

R5C3 can only be <6>

R5C2 can only be <7>

R8C3 can only be <2>

R9C2 can only be <3>

R3C2 can only be <9>

R8C2 can only be <6>

R1C1 is the only square in row 1 that can be <6>

R4C5 is the only square in row 4 that can be <7>

R6C6 is the only square in row 6 that can be <6>

R8C1 is the only square in row 8 that can be <5>

R9C1 can only be <7>

R8C9 is the only square in row 8 that can be <7>

R9C8 is the only square in row 9 that can be <8>

R2C1 is the only square in column 1 that can be <3>

Squares R2C7 and R7C7 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.

R5C7 - removing <2> from <239> leaving <39>

R8C7 - removing <1> from <139> leaving <39>

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.

R6C5 - removing <1> from <1348> leaving <348>

Intersection of column 6 with block 5. The value <4> 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 this value.

R5C5 - removing <4> from <2349> leaving <239>

R6C5 - removing <4> from <348> leaving <38>

Intersection of column 9 with block 6. The value <4> only appears in one or more of squares R4C9, R5C9 and R6C9 of column 9. These squares are the ones that intersect with block 6. Thus, the other (non-intersecting) squares of block 6 cannot contain this value.

R5C8 - removing <4> from <2349> leaving <239>

R5C6 is the only square in row 5 that can be <4>

R4C6 can only be <2>

R1C6 can only be <3>

R9C6 can only be <5>

R3C5 can only be <4>

R3C8 can only be <3>

R2C8 is the only square in row 2 that can be <4>

R5C8 is the only square in row 5 that can be <2>

R5C4 is the only square in row 5 that can be <5>

R8C7 is the only square in row 8 that can be <3>

R5C7 can only be <9>

R5C5 can only be <3>

R4C9 can only be <4>

R4C1 can only be <1>

R6C9 can only be <3>

R6C5 can only be <8>

R6C4 can only be <1>

R2C5 can only be <2>

R2C7 can only be <1>

R7C5 can only be <1>

R1C4 can only be <8>

R2C2 can only be <8>

R7C7 can only be <2>

R1C8 can only be <9>

R4C4 can only be <9>

R6C1 can only be <4>

R9C4 can only be <2>

R8C5 can only be <9>

R9C9 can only be <9>

R8C8 can only be <1>

R1C9 can only be <2>

R1C2 can only be <1>

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