Mar 13 - Very Hard
Puzzle Copyright © Kevin Stone
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Reasoning
R1C7 can only be <7>
R3C5 can only be <1>
R7C5 can only be <4>
R4C5 can only be <6>
R6C5 can only be <8>
R5C5 can only be <7>
R1C2 is the only square in row 1 that can be <5>
R5C3 is the only square in row 5 that can be <6>
R1C3 can only be <9>
R1C8 can only be <6>
R3C8 is the only square in row 3 that can be <9>
R7C1 is the only square in row 7 that can be <9>
R8C2 is the only square in row 8 that can be <2>
R9C8 is the only square in row 9 that can be <5>
R6C8 is the only square in column 8 that can be <2>
R8C8 is the only square in column 8 that can be <7>
Squares R8C4 and R8C6 in row 8 form a simple naked pair. These 2 squares both contain the 2 possibilities <39>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the row.
R8C7 - removing <3> from <1348> leaving <148>
R8C9 - removing <3> from <1346> leaving <146>
Squares R4C2 and R6C2 in column 2 form a simple naked pair. These 2 squares both contain the 2 possibilities <14>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the column.
R2C2 - removing <4> from <34678> leaving <3678>
R3C2 - removing <4> from <348> leaving <38>
R9C2 - removing <14> from <147> leaving <7>
R2C3 is the only square in row 2 that can be <7>
Squares R8C3 and R9C3 in block 7 form a simple naked pair. These 2 squares both contain the 2 possibilities <14>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the block.
R8C1 - removing <4> from <468> leaving <68>
Intersection of row 3 with block 1. The value <8> only appears in one or more of squares R3C1, R3C2 and R3C3 of row 3. These squares are the ones that intersect with block 1. Thus, the other (non-intersecting) squares of block 1 cannot contain this value.
R2C1 - removing <8> from <468> leaving <46>
R2C2 - removing <8> from <368> leaving <36>
Squares R9C3, R9C7, R8C3 and R8C7 form a Type-1 Unique Rectangle on <14>.
R8C7 - removing <14> from <148> leaving <8>
R8C1 can only be <6>
R7C8 can only be <3>
R7C9 can only be <6>
R4C8 can only be <1>
R7C2 can only be <8>
R2C1 can only be <4>
R3C1 can only be <8>
R3C2 can only be <3>
R3C9 can only be <4>
R2C2 can only be <6>
R8C9 can only be <1>
R4C2 can only be <4>
R2C8 can only be <8>
R5C7 can only be <3>
R5C4 can only be <2>
R2C7 can only be <1>
R8C3 can only be <4>
R2C9 can only be <3>
R9C7 can only be <4>
R9C3 can only be <1>
R6C2 can only be <1>
R5C6 can only be <1>
R2C4 can only be <5>
R6C6 can only be <9>
R6C4 can only be <4>
R8C6 can only be <3>
R8C4 can only be <9>
R4C6 can only be <5>
R2C6 can only be <2>
R4C4 can only be <3>
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