Aug 06 - Hard
Puzzle Copyright © Kevin Stone
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Reasoning
R5C7 can only be <5>
R3C5 is the only square in row 3 that can be <5>
R2C9 is the only square in row 2 that can be <5>
R9C1 is the only square in row 9 that can be <5>
R4C1 is the only square in column 1 that can be <6>
R6C6 is the only square in block 5 that can be <2>
R6C5 is the only square in row 6 that can be <6>
R6C8 is the only square in row 6 that can be <9>
R3C7 is the only square in row 3 that can be <9>
R3C8 is the only square in row 3 that can be <2>
R3C6 is the only square in row 3 that can be <3>
R4C5 is the only square in row 4 that can be <9>
R9C7 is the only square in block 9 that can be <6>
R7C4 is the only square in column 4 that can be <6>
R8C7 is the only square in column 7 that can be <2>
R8C8 is the only square in row 8 that can be <3>
R9C4 is the only square in column 4 that can be <2>
Squares R7C9 and R9C9 in column 9 form a simple naked pair. These 2 squares both contain the 2 possibilities <47>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the column.
R1C9 - removing <7> from <137> leaving <13>
R6C9 - removing <4> from <134> leaving <13>
Intersection of row 2 with block 1. The values <39> 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 these values.
R1C3 - removing <3> from <1348> leaving <148>
Intersection of row 6 with block 4. The value <4> only appears in one or more of squares R6C1, R6C2 and R6C3 of row 6. These squares are the ones that intersect with block 4. Thus, the other (non-intersecting) squares of block 4 cannot contain this value.
R4C2 - removing <4> from <348> leaving <38>
R5C2 - removing <4> from <1248> leaving <128>
R5C3 - removing <4> from <1248> leaving <128>
Intersection of row 9 with block 7. The value <1> 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.
R8C1 - removing <1> from <148> leaving <48>
R8C2 - removing <1> from <1478> leaving <478>
Intersection of column 1 with block 1. The value <1> 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 <1> from <148> leaving <48>
R2C2 - removing <1> from <1389> leaving <389>
R2C3 - removing <1> from <1389> leaving <389>
Squares R1C1<148>, R1C3<48> and R3C1<14> in block 1 form a comprehensive naked triplet. These 3 squares can only contain the 3 possibilities <148>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the block.
R2C2 - removing <8> from <389> leaving <39>
R2C3 - removing <8> from <389> leaving <39>
Intersection of row 2 with block 2. The value <8> only appears in one or more of squares R2C4, R2C5 and R2C6 of row 2. These squares are the ones that intersect with block 2. Thus, the other (non-intersecting) squares of block 2 cannot contain this value.
R1C6 - removing <8> from <468> leaving <46>
Squares R7C5<478>, R7C6<48> and R7C9<47> in row 7 form a comprehensive naked triplet. These 3 squares can only contain the 3 possibilities <478>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the row.
R7C2 - removing <478> from <24789> leaving <29>
R7C3 - removing <48> from <2489> leaving <29>
Intersection of row 7 with block 8. The value <8> 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.
R8C4 - removing <8> from <148> leaving <14>
R8C5 - removing <8> from <1478> leaving <147>
R4C4 is the only square in column 4 that can be <8>
R4C2 can only be <3>
R5C5 can only be <4>
R5C8 can only be <1>
R2C8 can only be <6>
R6C9 can only be <3>
R1C9 can only be <1>
R4C7 can only be <7>
R2C6 can only be <8>
R1C8 can only be <7>
R2C2 can only be <9>
R4C8 can only be <4>
R1C7 can only be <3>
R2C3 can only be <3>
R7C2 can only be <2>
R2C5 can only be <1>
R7C6 can only be <4>
R7C3 can only be <9>
R5C2 can only be <8>
R7C9 can only be <7>
R1C6 can only be <6>
R8C4 can only be <1>
R7C5 can only be <8>
R9C9 can only be <4>
R8C5 can only be <7>
R3C4 can only be <4>
R9C3 can only be <1>
R3C1 can only be <1>
R5C3 can only be <2>
R8C2 can only be <4>
R8C1 can only be <8>
R6C2 can only be <1>
R9C2 can only be <7>
R6C3 can only be <4>
R1C3 can only be <8>
R1C1 can only be <4>
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