Aug 22 - Very Hard
Puzzle Copyright © Kevin Stone
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Reasoning
R1C6 can only be <5>
R9C4 can only be <4>
R6C6 can only be <1>
R1C5 is the only square in row 1 that can be <4>
R5C5 is the only square in row 5 that can be <2>
R5C2 is the only square in row 5 that can be <9>
R5C3 is the only square in row 5 that can be <3>
R1C2 is the only square in row 1 that can be <3>
R8C3 is the only square in column 3 that can be <4>
Squares R2C5 and R6C5 in column 5 form a simple naked pair. These 2 squares both contain the 2 possibilities <69>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the column.
R4C5 - removing <6> from <368> leaving <38>
Squares R4C5 and R4C6 in row 4 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 row.
R4C8 - removing <8> from <4568> leaving <456>
Squares R1C3<27>, R2C3<57> and R3C2<25> in block 1 form a comprehensive naked triplet. These 3 squares can only contain the 3 possibilities <257>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the block.
R2C2 - removing <57> from <1567> leaving <16>
Intersection of column 2 with block 7. The values <78> 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.
R9C3 - removing <7> from <257> leaving <25>
Squares R5C1 and R9C1 in column 1 and R5C9 and R9C9 in column 9 form a Simple X-Wing pattern on possibility <5>. All other instances of this possibility in rows 5 and 9 can be removed.
R9C2 - removing <5> from <12578> leaving <1278>
R9C3 - removing <5> from <25> leaving <2>
R5C7 - removing <5> from <1568> leaving <168>
R9C7 - removing <5> from <5678> leaving <678>
R5C8 - removing <5> from <1568> leaving <168>
R9C8 - removing <5> from <356789> leaving <36789>
R1C3 can only be <7>
R2C3 can only be <5>
R3C2 can only be <2>
R3C8 can only be <5>
R1C8 is the only square in row 1 that can be <2>
R8C7 is the only square in column 7 that can be <5>
R9C1 is the only square in row 9 that can be <5>
R5C1 can only be <6>
R1C1 can only be <1>
R1C7 can only be <8>
R2C2 can only be <6>
R1C9 can only be <9>
R5C7 can only be <1>
R1C4 can only be <6>
R9C9 can only be <8>
R2C5 can only be <9>
R6C5 can only be <6>
R5C8 can only be <8>
R2C7 can only be <7>
R5C9 can only be <5>
R7C8 can only be <7>
R6C8 can only be <4>
R4C4 can only be <5>
R6C2 can only be <5>
R4C8 can only be <6>
R7C2 can only be <8>
R2C8 can only be <1>
R8C8 can only be <3>
R9C7 can only be <6>
R9C8 can only be <9>
R9C6 can only be <3>
R4C2 can only be <4>
R6C4 can only be <9>
R8C2 can only be <7>
R8C5 can only be <8>
R9C2 can only be <1>
R4C5 can only be <3>
R9C5 can only be <7>
R4C6 can only be <8>
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