Sep 21 - Very Hard
Puzzle Copyright © Kevin Stone
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Reasoning
R7C4 is the only square in row 7 that can be <3>
R4C5 is the only square in row 4 that can be <3>
R9C9 is the only square in row 9 that can be <3>
R7C6 is the only square in block 8 that can be <5>
Squares R1C2 and R1C5 in row 1 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 row.
R1C1 - removing <1> from <189> leaving <89>
R5C1 is the only square in column 1 that can be <1>
Squares R8C5 and R9C5 in column 5 form a simple naked pair. These 2 squares both contain the 2 possibilities <29>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the column.
R5C5 - removing <29> from <24679> leaving <467>
R6C5 - removing <29> from <1269> leaving <16>
Squares R3C6 and R4C6 in column 6 form a simple naked pair. These 2 squares both contain the 2 possibilities <78>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the column.
R5C6 - removing <7> from <279> leaving <29>
Intersection of block 2 with row 3. The value <8> only appears in one or more of squares R3C4, R3C5 and R3C6 of block 2. These squares are the ones that intersect with row 3. Thus, the other (non-intersecting) squares of row 3 cannot contain this value.
R3C3 - removing <8> from <14689> leaving <1469>
R3C8 - removing <8> from <6789> leaving <679>
Squares R3C2 and R5C2 in column 2 and R3C8 and R5C8 in column 8 form a Simple X-Wing pattern on possibility <6>. All other instances of this possibility in rows 3 and 5 can be removed.
R3C3 - removing <6> from <1469> leaving <149>
R5C5 - removing <6> from <467> leaving <47>
R3C7 - removing <6> from <4679> leaving <479>
R6C5 is the only square in column 5 that can be <6>
R6C3 can only be <2>
R6C6 can only be <9>
R6C7 can only be <5>
R5C6 can only be <2>
R6C4 can only be <1>
R2C1 is the only square in row 2 that can be <2>
R5C4 is the only square in row 5 that can be <5>
R8C9 is the only square in row 8 that can be <5>
R1C8 is the only square in row 1 that can be <5>
R8C1 is the only square in column 1 that can be <6>
R8C3 is the only square in row 8 that can be <8>
R9C1 can only be <9>
R9C5 can only be <2>
R1C1 can only be <8>
R7C3 can only be <1>
R9C2 can only be <7>
R8C5 can only be <9>
R1C9 can only be <9>
R5C9 can only be <7>
R5C5 can only be <4>
R2C9 can only be <8>
R4C7 can only be <6>
R8C7 can only be <2>
R9C8 can only be <8>
R7C2 can only be <2>
R4C3 can only be <4>
R5C8 can only be <9>
R5C2 can only be <6>
R1C5 can only be <1>
R2C5 can only be <7>
R4C4 can only be <8>
R7C8 can only be <7>
R7C7 can only be <9>
R3C8 can only be <6>
R1C2 can only be <4>
R2C7 can only be <4>
R3C6 can only be <8>
R2C3 can only be <6>
R3C7 can only be <7>
R3C4 can only be <4>
R4C6 can only be <7>
R3C3 can only be <9>
R3C2 can only be <1>
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