Aug 10 - Very Hard
Puzzle Copyright © Kevin Stone
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Reasoning
R2C1 is the only square in row 2 that can be <8>
R3C3 is the only square in row 3 that can be <3>
R5C1 is the only square in row 5 that can be <5>
R1C1 can only be <7>
R1C2 can only be <5>
R7C3 is the only square in row 7 that can be <9>
R9C5 is the only square in row 9 that can be <5>
R3C6 is the only square in row 3 that can be <5>
R9C8 is the only square in row 9 that can be <8>
R4C3 is the only square in column 3 that can be <7>
R9C2 is the only square in column 2 that can be <7>
R4C8 is the only square in column 8 that can be <1>
R5C5 is the only square in column 5 that can be <1>
Intersection of row 3 with block 2. The value <2> 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.
R1C5 - removing <2> from <249> leaving <49>
Intersection of column 7 with block 6. The values <89> only appears in one or more of squares R4C7, R5C7 and R6C7 of column 7. These squares are the ones that intersect with block 6. Thus, the other (non-intersecting) squares of block 6 cannot contain these values.
R5C9 - removing <9> from <2349> leaving <234>
Squares R2C4 and R2C9 in row 2 and R8C4 and R8C9 in row 8 form a Simple X-Wing pattern on possibility <7>. All other instances of this possibility in columns 4 and 9 can be removed.
R3C4 - removing <7> from <247> leaving <24>
R7C4 - removing <7> from <2347> leaving <234>
Squares R3C4<24>, R5C4<234> and R7C4<234> in column 4 form a comprehensive naked triplet. These 3 squares can only contain the 3 possibilities <234>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the column.
R8C4 - removing <34> from <1347> leaving <17>
Intersection of block 8 with row 7. The values <23> only appears in one or more of squares R7C4, R7C5 and R7C6 of block 8. These squares are the ones that intersect with row 7. Thus, the other (non-intersecting) squares of row 7 cannot contain these values.
R7C7 - removing <3> from <347> leaving <47>
Squares R3C7 and R7C7 in column 7 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.
R4C7 - removing <4> from <349> leaving <39>
R5C7 - removing <4> from <3489> leaving <389>
R6C7 - removing <4> from <3489> leaving <389>
R4C5 is the only square in row 4 that can be <4>
R1C5 can only be <9>
R2C6 can only be <1>
R2C4 can only be <7>
R8C6 can only be <4>
R8C1 can only be <3>
R7C6 can only be <2>
R2C9 can only be <9>
R8C4 can only be <1>
R3C5 can only be <2>
R3C4 can only be <4>
R6C5 can only be <3>
R6C2 can only be <9>
R7C5 can only be <7>
R5C4 can only be <2>
R7C7 can only be <4>
R7C4 can only be <3>
R5C6 can only be <9>
R3C7 can only be <7>
R9C9 can only be <3>
R8C9 can only be <7>
R9C1 can only be <4>
R5C9 can only be <4>
R5C3 can only be <8>
R1C9 can only be <2>
R6C8 can only be <2>
R6C7 can only be <8>
R4C2 can only be <3>
R6C3 can only be <4>
R5C7 can only be <3>
R1C8 can only be <4>
R4C7 can only be <9>
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