Mar 17 - Very Hard
Puzzle Copyright © Kevin Stone
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Reasoning
R5C7 is the only square in row 5 that can be <1>
R2C9 is the only square in row 2 that can be <1>
R1C4 is the only square in row 1 that can be <1>
R1C6 is the only square in row 1 that can be <4>
R8C5 is the only square in row 8 that can be <7>
R2C1 is the only square in row 2 that can be <7>
R8C9 is the only square in row 8 that can be <9>
R9C4 is the only square in row 9 that can be <9>
R8C7 is the only square in column 7 that can be <5>
R8C1 can only be <4>
R8C3 can only be <8>
R9C8 is the only square in row 9 that can be <4>
Intersection of column 2 with block 7. The value <5> 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 this value.
R9C1 - removing <5> from <235> leaving <23>
Intersection of block 5 with column 5. The values <59> only appears in one or more of squares R4C5, R5C5 and R6C5 of block 5. These squares are the ones that intersect with column 5. Thus, the other (non-intersecting) squares of column 5 cannot contain these values.
R3C5 - removing <5> from <358> leaving <38>
R7C5 - removing <5> from <4568> leaving <468>
Squares R2C5 and R3C5 in column 5 form a simple naked pair. These 2 squares both contain the 2 possibilities <38>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the column.
R7C5 - removing <8> from <468> leaving <46>
Squares R2C5 and R3C5 in block 2 form a simple naked pair. These 2 squares both contain the 2 possibilities <38>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the block.
R3C6 - removing <8> from <578> leaving <57>
Squares R6C3<46>, R6C7<48> and R6C9<68> in row 6 form a comprehensive naked triplet. These 3 squares can only contain the 3 possibilities <468>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the row.
R6C5 - removing <46> from <4569> leaving <59>
Squares R3C2 and R3C8 in row 3 and R7C2 and R7C8 in row 7 form a Simple X-Wing pattern on possibility <2>. All other instances of this possibility in columns 2 and 8 can be removed.
R5C2 - removing <2> from <239> leaving <39>
R5C8 - removing <2> from <236> leaving <36>
R9C2 - removing <2> from <235> leaving <35>
R5C3 is the only square in row 5 that can be <2>
R2C3 can only be <3>
R2C5 can only be <8>
R1C1 can only be <9>
R2C7 can only be <2>
R3C5 can only be <3>
R4C7 can only be <4>
R3C8 can only be <8>
R3C2 can only be <2>
R7C8 can only be <2>
R4C3 can only be <6>
R6C7 can only be <8>
R6C9 can only be <6>
R6C3 can only be <4>
R1C9 can only be <3>
R5C8 can only be <3>
R7C2 can only be <5>
R9C9 can only be <8>
R9C6 can only be <5>
R1C2 can only be <8>
R6C1 can only be <5>
R1C8 can only be <6>
R4C9 can only be <2>
R4C5 can only be <5>
R4C1 can only be <3>
R6C5 can only be <9>
R5C2 can only be <9>
R7C4 can only be <4>
R9C2 can only be <3>
R7C5 can only be <6>
R5C4 can only be <7>
R7C6 can only be <8>
R5C5 can only be <4>
R9C1 can only be <2>
R3C6 can only be <7>
R3C4 can only be <5>
R5C6 can only be <6>
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