Sep 13 - Very Hard
Puzzle Copyright © Kevin Stone
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Reasoning
R2C4 is the only square in row 2 that can be <6>
R3C5 is the only square in row 3 that can be <3>
R2C2 is the only square in row 2 that can be <3>
R9C8 is the only square in row 9 that can be <2>
R7C1 is the only square in row 7 that can be <2>
R5C7 is the only square in column 7 that can be <3>
R4C9 is the only square in column 9 that can be <2>
R6C9 is the only square in column 9 that can be <6>
Squares R4C8 and R6C8 in column 8 form a simple naked pair. These 2 squares both contain the 2 possibilities <48>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the column.
R1C8 - removing <48> from <4589> leaving <59>
R2C8 - removing <48> from <4578> leaving <57>
R2C6 is the only square in row 2 that can be <8>
Squares R1C4 and R1C6 in row 1 form a simple naked pair. These 2 squares both contain the 2 possibilities <24>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the row.
R1C2 - removing <4> from <148> leaving <18>
R1C7 - removing <4> from <1489> leaving <189>
Squares R1C4 and R5C4 in column 4 form a simple naked pair. These 2 squares both contain the 2 possibilities <24>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the column.
R4C4 - removing <4> from <489> leaving <89>
R6C4 - removing <4> from <34789> leaving <3789>
R9C4 - removing <4> from <479> leaving <79>
Intersection of row 5 with block 5. The values <24> only appears in one or more of squares R5C4, R5C5 and R5C6 of row 5. These squares are the ones that intersect with block 5. Thus, the other (non-intersecting) squares of block 5 cannot contain these values.
R4C5 - removing <4> from <4689> leaving <689>
R4C6 - removing <4> from <145> leaving <15>
R6C5 - removing <4> from <489> leaving <89>
R6C6 - removing <4> from <1347> leaving <137>
Squares R4C4 and R6C5 in block 5 form a simple naked pair. These 2 squares both contain the 2 possibilities <89>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the block.
R4C5 - removing <89> from <689> leaving <6>
R6C4 - removing <89> from <3789> leaving <37>
R5C5 can only be <4>
R5C4 can only be <2>
R5C6 can only be <5>
R1C4 can only be <4>
R5C3 can only be <6>
R4C6 can only be <1>
R1C6 can only be <2>
R4C1 is the only square in row 4 that can be <5>
R9C2 is the only square in row 9 that can be <6>
R1C3 is the only square in column 3 that can be <5>
R1C8 can only be <9>
R9C6 is the only square in column 6 that can be <4>
Intersection of column 2 with block 4. The value <4> only appears in one or more of squares R4C2, R5C2 and R6C2 of column 2. These squares are the ones that intersect with block 4. Thus, the other (non-intersecting) squares of block 4 cannot contain this value.
R6C1 - removing <4> from <149> leaving <19>
Intersection of block 7 with row 8. The value <9> only appears in one or more of squares R8C1, R8C2 and R8C3 of block 7. These squares are the ones that intersect with row 8. Thus, the other (non-intersecting) squares of row 8 cannot contain this value.
R8C4 - removing <9> from <3789> leaving <378>
Squares R6C4, R6C6, R8C4 and R8C6 form a Type-1 Unique Rectangle on <37>.
R8C4 - removing <37> from <378> leaving <8>
R4C4 can only be <9>
R7C5 can only be <9>
R4C2 can only be <4>
R9C4 can only be <7>
R6C5 can only be <8>
R6C8 can only be <4>
R4C8 can only be <8>
R7C7 can only be <4>
R7C9 can only be <7>
R7C3 can only be <8>
R8C8 can only be <5>
R8C9 can only be <1>
R2C8 can only be <7>
R8C2 can only be <9>
R3C9 can only be <4>
R9C7 can only be <9>
R9C3 can only be <1>
R6C4 can only be <3>
R8C6 can only be <3>
R2C1 can only be <4>
R2C9 can only be <5>
R6C6 can only be <7>
R8C1 can only be <7>
R6C2 can only be <1>
R3C3 can only be <7>
R3C1 can only be <1>
R6C1 can only be <9>
R1C2 can only be <8>
R1C7 can only be <1>
R3C7 can only be <8>
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