Jul 07 - Very Hard
Puzzle Copyright © Kevin Stone
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Reasoning
R8C8 is the only square in row 8 that can be <2>
R8C4 is the only square in row 8 that can be <7>
R1C6 is the only square in row 1 that can be <7>
R7C7 is the only square in row 7 that can be <7>
R6C8 is the only square in row 6 that can be <7>
R4C3 is the only square in row 4 that can be <7>
R9C5 is the only square in row 9 that can be <6>
R5C3 is the only square in column 3 that can be <2>
R4C9 is the only square in row 4 that can be <2>
R9C8 is the only square in block 9 that can be <3>
R8C3 is the only square in column 3 that can be <3>
Squares R9C3 and R9C9 in row 9 form a simple naked pair. These 2 squares both contain the 2 possibilities <18>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the row.
R9C6 - removing <1> from <145> leaving <45>
Squares R7C9 and R9C9 in column 9 form a simple naked pair. These 2 squares both contain the 2 possibilities <18>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the column.
R5C9 - removing <18> from <1568> leaving <56>
Squares R2C6<345>, R2C7<36>, R2C8<45> and R2C9<56> in row 2 form a comprehensive naked quad. These 4 squares can only contain the 4 possibilities <3456>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the row.
R2C2 - removing <6> from <268> leaving <28>
R2C5 - removing <345> from <23458> leaving <28>
Intersection of row 2 with block 3. The value <6> only appears in one or more of squares R2C7, R2C8 and R2C9 of row 2. These squares are the ones that intersect with block 3. Thus, the other (non-intersecting) squares of block 3 cannot contain this value.
R1C7 - removing <6> from <136> leaving <13>
Squares R2C2 and R2C5 in row 2 and R4C2 and R4C5 in row 4 form a Simple X-Wing pattern on possibility <8>. All other instances of this possibility in columns 2 and 5 can be removed.
R3C5 - removing <8> from <4589> leaving <459>
R6C2 - removing <8> from <1589> leaving <159>
R6C5 - removing <8> from <14589> leaving <1459>
R7C2 - removing <8> from <189> leaving <19>
R7C9 is the only square in row 7 that can be <8>
R9C9 can only be <1>
R9C3 can only be <8>
R3C3 can only be <1>
R1C7 is the only square in row 1 that can be <1>
R6C7 can only be <8>
R5C7 can only be <6>
R5C9 can only be <5>
R2C7 can only be <3>
R2C9 can only be <6>
R4C8 can only be <1>
Squares R2C6 and R9C6 in column 6 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 column.
R4C6 - removing <5> from <59> leaving <9>
R3C4 is the only square in column 4 that can be <9>
R3C1 is the only square in row 3 that can be <8>
R5C1 can only be <1>
R2C2 can only be <2>
R5C6 can only be <3>
R6C1 can only be <9>
R5C4 can only be <8>
R7C6 can only be <1>
R6C2 can only be <5>
R8C1 can only be <6>
R6C4 can only be <4>
R4C2 can only be <8>
R6C5 can only be <1>
R1C4 can only be <3>
R9C4 can only be <5>
R8C5 can only be <9>
R7C2 can only be <9>
R1C1 can only be <4>
R8C2 can only be <1>
R7C5 can only be <3>
R9C6 can only be <4>
R2C6 can only be <5>
R1C5 can only be <2>
R1C2 can only be <6>
R2C5 can only be <8>
R4C5 can only be <5>
R2C8 can only be <4>
R3C5 can only be <4>
R3C8 can only be <5>
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