Jul 28 - Hard
Puzzle Copyright © Kevin Stone
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Reasoning
R1C6 is the only square in row 1 that can be <8>
R2C7 is the only square in row 2 that can be <6>
R2C8 is the only square in row 2 that can be <7>
R4C2 is the only square in column 2 that can be <1>
R4C9 can only be <6>
R3C5 is the only square in column 5 that can be <1>
R1C9 is the only square in column 9 that can be <9>
Intersection of row 2 with block 1. The value <3> only appears in one or more of squares R2C1, R2C2 and R2C3 of row 2. These squares are the ones that intersect with block 1. Thus, the other (non-intersecting) squares of block 1 cannot contain this value.
R3C1 - removing <3> from <2349> leaving <249>
Intersection of column 1 with block 1. The value <2> only appears in one or more of squares R1C1, R2C1 and R3C1 of column 1. These squares are the ones that intersect with block 1. Thus, the other (non-intersecting) squares of block 1 cannot contain this value.
R1C3 - removing <2> from <24> leaving <4>
R3C8 is the only square in block 3 that can be <4>
R3C7 is the only square in row 3 that can be <3>
R9C7 can only be <7>
R7C4 is the only square in row 7 that can be <7>
Squares R7C2 and R7C9 in row 7 form a simple naked pair. These 2 squares both contain the 2 possibilities <34>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the row.
R7C5 - removing <3> from <235> leaving <25>
Intersection of row 9 with block 7. The value <3> only appears in one or more of squares R9C1, R9C2 and R9C3 of row 9. These squares are the ones that intersect with block 7. Thus, the other (non-intersecting) squares of block 7 cannot contain this value.
R7C2 - removing <3> from <34> leaving <4>
R8C2 - removing <3> from <34689> leaving <4689>
R7C9 can only be <3>
R6C9 can only be <7>
R8C8 can only be <1>
R8C9 can only be <4>
R1C8 can only be <2>
R1C7 can only be <1>
R4C8 can only be <5>
R6C8 can only be <3>
R5C9 can only be <1>
R5C7 can only be <8>
R4C7 can only be <2>
R5C3 is the only square in row 5 that can be <7>
R5C5 is the only square in row 5 that can be <6>
R5C6 is the only square in row 5 that can be <3>
R8C5 is the only square in row 8 that can be <3>
R2C6 is the only square in column 6 that can be <4>
R6C6 is the only square in column 6 that can be <5>
R5C4 can only be <4>
R5C1 can only be <5>
R4C1 is the only square in row 4 that can be <4>
R6C5 is the only square in row 6 that can be <2>
R7C5 can only be <5>
R7C3 can only be <2>
R2C5 can only be <9>
R2C2 can only be <3>
R4C5 can only be <8>
R3C6 can only be <2>
R3C1 can only be <9>
R8C6 can only be <9>
R2C4 can only be <5>
R4C4 can only be <9>
R8C3 can only be <6>
R9C4 can only be <8>
R8C4 can only be <2>
R2C1 can only be <2>
R9C2 can only be <9>
R6C1 can only be <8>
R9C1 can only be <3>
R8C2 can only be <8>
R6C3 can only be <9>
R9C3 can only be <5>
R6C2 can only be <6>
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