Jul 02 - Very Hard
Puzzle Copyright © Kevin Stone
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Reasoning
R3C3 is the only square in row 3 that can be <8>
R1C7 is the only square in row 1 that can be <8>
R5C2 is the only square in row 5 that can be <8>
R4C6 is the only square in row 4 that can be <8>
R4C4 is the only square in column 4 that can be <3>
R9C5 is the only square in column 5 that can be <6>
Intersection of row 3 with block 2. The value <7> only appears in one or more of squares R3C4, R3C5 and R3C6 of row 3. These squares are the ones that intersect with block 2. Thus, the other (non-intersecting) squares of block 2 cannot contain this value.
R1C4 - removing <7> from <1479> leaving <149>
R1C5 - removing <7> from <179> leaving <19>
R2C6 - removing <7> from <14579> leaving <1459>
R1C2 is the only square in row 1 that can be <7>
R8C2 is the only square in column 2 that can be <6>
R6C5 is the only square in column 5 that can be <7>
R7C7 is the only square in column 7 that can be <6>
R7C1 is the only square in row 7 that can be <3>
R1C3 is the only square in row 1 that can be <3>
R2C3 is the only square in column 3 that can be <1>
R2C1 is the only square in row 2 that can be <2>
R6C3 is the only square in column 3 that can be <6>
R6C8 is the only square in row 6 that can be <2>
R4C3 is the only square in row 4 that can be <2>
R9C9 is the only square in row 9 that can be <2>
R8C8 is the only square in column 8 that can be <1>
Squares R2C7 and R2C8 in row 2 form a simple naked pair. These 2 squares both contain the 2 possibilities <47>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the row.
R2C6 - removing <4> from <459> leaving <59>
R6C6 is the only square in column 6 that can be <4>
R9C1 is the only square in column 1 that can be <4>
R5C3 is the only square in column 3 that can be <4>
R5C8 can only be <3>
R9C8 can only be <7>
R2C8 can only be <4>
R2C7 can only be <7>
R1C4 is the only square in row 1 that can be <4>
R8C4 is the only square in row 8 that can be <7>
R3C6 is the only square in row 3 that can be <7>
R9C7 is the only square in row 9 that can be <3>
R7C6 is the only square in column 6 that can be <1>
Squares R1C9 and R3C9 in column 9 form a simple naked pair. These 2 squares both contain the 2 possibilities <16>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the column.
R4C9 - removing <1> from <1459> leaving <459>
Intersection of column 5 with block 5. The value <5> only appears in one or more of squares R4C5, R5C5 and R6C5 of column 5. These squares are the ones that intersect with block 5. Thus, the other (non-intersecting) squares of block 5 cannot contain this value.
R6C4 - removing <5> from <159> leaving <19>
Squares R4C2 and R7C9 form a remote naked pair. <59> can be removed from any square that is common to their groups.
R4C9 - removing <59> from <459> leaving <4>
R8C7 is the only square in row 8 that can be <4>
Squares R6C1 and R7C4 form a remote naked pair. <59> can be removed from any square that is common to their groups.
R6C4 - removing <9> from <19> leaving <1>
R3C4 can only be <5>
R3C1 can only be <6>
R7C4 can only be <9>
R2C6 can only be <9>
R7C9 can only be <5>
R9C6 can only be <5>
R8C9 can only be <9>
R8C3 can only be <5>
R9C3 can only be <9>
R2C2 can only be <5>
R1C5 can only be <1>
R3C9 can only be <1>
R1C1 can only be <9>
R1C9 can only be <6>
R6C1 can only be <5>
R4C2 can only be <9>
R4C5 can only be <5>
R4C7 can only be <1>
R5C5 can only be <9>
R5C7 can only be <5>
R6C7 can only be <9>
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