Jun 13 - Very Hard
Puzzle Copyright © Kevin Stone
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Reasoning
R1C4 is the only square in row 1 that can be <7>
R4C4 can only be <4>
R2C8 is the only square in row 2 that can be <8>
R6C6 is the only square in row 6 that can be <8>
R9C1 is the only square in row 9 that can be <8>
Squares R2C2 and R2C5 in row 2 form a simple naked pair. These 2 squares both contain the 2 possibilities <45>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the row.
R2C1 - removing <4> from <134> leaving <13>
R2C9 - removing <45> from <1345> leaving <13>
Squares R7C9<257>, R8C8<24>, R9C7<27> and R9C8<245> in block 9 form a comprehensive naked quad. These 4 squares can only contain the 4 possibilities <2457>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the block.
R8C9 - removing <24> from <2469> leaving <69>
R9C9 - removing <2457> from <245679> leaving <69>
Intersection of column 9 with block 3. The value <4> only appears in one or more of squares R1C9, R2C9 and R3C9 of column 9. These squares are the ones that intersect with block 3. Thus, the other (non-intersecting) squares of block 3 cannot contain this value.
R1C8 - removing <4> from <1245> leaving <125>
Squares R3C5 and R3C9 in row 3 and R7C5 and R7C9 in row 7 form a Simple X-Wing pattern on possibility <5>. All other instances of this possibility in columns 5 and 9 can be removed.
R1C9 - removing <5> from <12345> leaving <1234>
R2C5 - removing <5> from <45> leaving <4>
R6C5 - removing <5> from <579> leaving <79>
R2C2 can only be <5>
R6C4 is the only square in row 6 that can be <5>
R9C4 can only be <9>
R9C9 can only be <6>
R5C4 can only be <1>
R8C9 can only be <9>
R5C8 can only be <2>
R8C8 can only be <4>
R8C2 can only be <6>
R9C8 can only be <5>
R1C8 can only be <1>
R2C9 can only be <3>
R2C1 can only be <1>
R4C9 can only be <7>
R1C7 can only be <2>
R4C1 can only be <6>
R6C9 can only be <1>
R7C9 can only be <2>
R5C7 can only be <3>
R5C6 can only be <6>
R7C1 can only be <7>
R7C5 can only be <5>
R1C9 can only be <4>
R9C7 can only be <7>
R9C2 can only be <4>
R1C2 can only be <9>
R3C9 can only be <5>
R3C5 can only be <6>
R3C1 can only be <4>
R5C3 can only be <4>
R9C3 can only be <3>
R1C6 can only be <5>
R6C1 can only be <9>
R9C6 can only be <2>
R1C3 can only be <6>
R8C1 can only be <2>
R4C6 can only be <3>
R8C5 can only be <3>
R1C1 can only be <3>
R5C2 can only be <7>
R4C5 can only be <2>
R5C5 can only be <9>
R6C5 can only be <7>
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