Jul 31 - Hard
Puzzle Copyright © Kevin Stone
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Reasoning
R2C8 is the only square in row 2 that can be <8>
R7C2 is the only square in row 7 that can be <2>
R6C1 is the only square in column 1 that can be <8>
R6C6 is the only square in row 6 that can be <9>
R2C5 is the only square in column 5 that can be <2>
Squares R1C1 and R7C1 in column 1 form a simple naked pair. These 2 squares both contain the 2 possibilities <46>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the column.
R2C1 - removing <4> from <149> leaving <19>
R4C1 - removing <4> from <149> leaving <19>
Intersection of row 3 with block 2. The value <1> only appears in one or more of squares R3C4, R3C5 and R3C6 of row 3. These squares are the ones that intersect with block 2. Thus, the other (non-intersecting) squares of block 2 cannot contain this value.
R2C4 - removing <1> from <1345> leaving <345>
Intersection of row 4 with block 5. The value <7> 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 this value.
R5C4 - removing <7> from <13478> leaving <1348>
R5C5 - removing <7> from <1347> leaving <134>
R5C6 - removing <7> from <13478> leaving <1348>
Intersection of row 6 with block 6. The value <6> only appears in one or more of squares R6C7, R6C8 and R6C9 of row 6. These squares are the ones that intersect with block 6. Thus, the other (non-intersecting) squares of block 6 cannot contain this value.
R5C7 - removing <6> from <467> leaving <47>
R5C8 - removing <6> from <1567> leaving <157>
Intersection of row 7 with block 8. The value <3> 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 this value.
R9C4 - removing <3> from <378> leaving <78>
R9C5 - removing <3> from <37> leaving <7>
R9C4 can only be <8>
R1C6 is the only square in row 1 that can be <7>
R1C3 is the only square in row 1 that can be <5>
R2C4 is the only square in row 2 that can be <5>
R4C4 is the only square in row 4 that can be <7>
R4C9 is the only square in row 4 that can be <2>
R8C9 can only be <5>
R7C8 can only be <6>
R7C1 can only be <4>
R3C8 can only be <9>
R6C8 can only be <1>
R9C9 can only be <3>
R9C7 can only be <9>
R8C8 can only be <7>
R7C4 can only be <3>
R1C1 can only be <6>
R8C2 can only be <9>
R7C6 can only be <5>
R8C3 can only be <8>
R9C3 can only be <6>
R8C7 can only be <2>
R5C8 can only be <5>
R3C9 is the only square in row 3 that can be <6>
R6C9 can only be <4>
R6C4 can only be <2>
R6C7 can only be <6>
R5C7 can only be <7>
R4C2 is the only square in row 4 that can be <5>
R5C2 is the only square in row 5 that can be <6>
R5C6 is the only square in row 5 that can be <8>
R5C5 is the only square in row 5 that can be <3>
R1C5 can only be <4>
R1C7 can only be <3>
R8C5 can only be <1>
R3C4 can only be <1>
R2C7 can only be <4>
R2C2 can only be <3>
R3C6 can only be <3>
R5C4 can only be <4>
R3C2 can only be <4>
R5C3 can only be <1>
R4C6 can only be <1>
R8C6 can only be <4>
R4C1 can only be <9>
R2C3 can only be <9>
R2C1 can only be <1>
R4C3 can only be <4>
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