Aug 24 - Very Hard
Puzzle Copyright © Kevin Stone
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Reasoning
R5C5 can only be <3>
R3C3 is the only square in row 3 that can be <6>
R6C7 is the only square in row 6 that can be <8>
R6C1 is the only square in row 6 that can be <3>
R9C5 is the only square in row 9 that can be <6>
R7C7 is the only square in row 7 that can be <6>
R2C4 is the only square in column 4 that can be <9>
R7C3 is the only square in column 3 that can be <9>
R9C9 is the only square in row 9 that can be <9>
R1C8 is the only square in row 1 that can be <9>
R3C2 is the only square in row 3 that can be <9>
R5C7 is the only square in row 5 that can be <9>
Squares R6C4 and R9C4 in column 4 form a simple naked pair. These 2 squares both contain the 2 possibilities <17>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the column.
R7C4 - removing <17> from <1347> leaving <34>
R8C4 - removing <17> from <1347> leaving <34>
Squares R7C4 and R8C4 in block 8 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 block.
R8C6 - removing <34> from <13478> leaving <178>
Intersection of row 9 with block 7. The value <2> 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.
R8C2 - removing <2> from <2347> leaving <347>
R8C3 - removing <2> from <12457> leaving <1457>
Intersection of column 1 with block 7. The value <1> only appears in one or more of squares R7C1, R8C1 and R9C1 of column 1. These squares are the ones that intersect with block 7. Thus, the other (non-intersecting) squares of block 7 cannot contain this value.
R8C3 - removing <1> from <1457> leaving <457>
Intersection of column 2 with block 7. The values <37> only appears in one or more of squares R7C2, R8C2 and R9C2 of column 2. These squares are the ones that intersect with block 7. Thus, the other (non-intersecting) squares of block 7 cannot contain these values.
R7C1 - removing <7> from <1457> leaving <145>
R8C3 - removing <7> from <457> leaving <45>
R9C1 - removing <7> from <127> leaving <12>
Intersection of column 3 with block 4. The values <17> only appears in one or more of squares R4C3, R5C3 and R6C3 of column 3. These squares are the ones that intersect with block 4. Thus, the other (non-intersecting) squares of block 4 cannot contain these values.
R5C1 - removing <7> from <247> leaving <24>
Intersection of column 8 with block 3. The value <4> only appears in one or more of squares R1C8, R2C8 and R3C8 of column 8. These squares are the ones that intersect with block 3. Thus, the other (non-intersecting) squares of block 3 cannot contain this value.
R1C9 - removing <4> from <478> leaving <78>
R3C9 - removing <4> from <13478> leaving <1378>
Squares R2C1<2458>, R2C2<24>, R2C3<245> and R2C8<248> in row 2 form a comprehensive naked quad. These 4 squares can only contain the 4 possibilities <2458>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the row.
R2C6 - removing <48> from <1348> leaving <13>
R2C7 - removing <2> from <123> leaving <13>
Squares R7C4, R8C4, R7C2 and R8C2 form a Type-2 Unique Rectangle on <34>.
R9C2 - removing <7> from <27> leaving <2>
R9C1 can only be <1>
R2C2 can only be <4>
R9C4 can only be <7>
R6C4 can only be <1>
R6C3 can only be <7>
R4C6 can only be <7>
R4C7 can only be <3>
R4C9 can only be <4>
R2C7 can only be <1>
R4C3 can only be <1>
R5C9 can only be <7>
R1C9 can only be <8>
R1C5 can only be <2>
R1C6 can only be <4>
R2C8 can only be <2>
R2C6 can only be <3>
R3C9 can only be <3>
R2C3 can only be <5>
R3C7 can only be <7>
R3C8 can only be <4>
R8C7 can only be <2>
R1C1 can only be <7>
R2C1 can only be <8>
R8C3 can only be <4>
R8C4 can only be <3>
R5C3 can only be <2>
R7C1 can only be <5>
R8C2 can only be <7>
R7C4 can only be <4>
R3C1 can only be <2>
R5C1 can only be <4>
R7C9 can only be <1>
R7C5 can only be <8>
R8C9 can only be <5>
R8C8 can only be <8>
R7C2 can only be <3>
R8C6 can only be <1>
R7C8 can only be <7>
R3C5 can only be <1>
R3C6 can only be <8>
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