Sep 11 - Very Hard
Puzzle Copyright © Kevin Stone
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Reasoning
R1C1 is the only square in row 1 that can be <8>
R5C1 can only be <7>
R5C7 can only be <1>
R1C2 is the only square in row 1 that can be <3>
R4C4 is the only square in row 4 that can be <8>
R5C3 is the only square in row 5 that can be <8>
R6C9 is the only square in row 6 that can be <5>
R7C3 is the only square in row 7 that can be <5>
R7C5 is the only square in row 7 that can be <8>
R8C7 is the only square in row 8 that can be <3>
R9C9 is the only square in row 9 that can be <8>
R5C5 is the only square in column 5 that can be <4>
R5C9 can only be <2>
R2C7 is the only square in column 7 that can be <5>
Intersection of row 3 with block 3. The value <7> only appears in one or more of squares R3C7, R3C8 and R3C9 of row 3. These squares are the ones that intersect with block 3. Thus, the other (non-intersecting) squares of block 3 cannot contain this value.
R2C9 - removing <7> from <179> leaving <19>
R4C9 is the only square in column 9 that can be <7>
R6C8 can only be <9>
R4C8 can only be <4>
R9C1 is the only square in row 9 that can be <4>
R8C9 is the only square in row 8 that can be <4>
R7C7 is the only square in block 9 that can be <9>
R3C7 can only be <7>
Squares R7C8 and R9C8 in column 8 form a simple naked pair. These 2 squares both contain the 2 possibilities <17>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the column.
R1C8 - removing <1> from <126> leaving <26>
R3C8 - removing <1> from <126> leaving <26>
R3C2 is the only square in row 3 that can be <1>
R7C2 can only be <7>
R7C8 can only be <1>
R9C8 can only be <7>
R8C1 is the only square in column 1 that can be <1>
Squares R9C2 and R9C5 in row 9 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 row.
R9C4 - removing <6> from <156> leaving <15>
R9C6 - removing <9> from <159> leaving <15>
Intersection of column 5 with block 2. The value <2> only appears in one or more of squares R1C5, R2C5 and R3C5 of column 5. 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 <2> from <1256> leaving <156>
R1C6 - removing <2> from <1259> leaving <159>
R2C4 - removing <2> from <1267> leaving <167>
R2C6 - removing <2> from <1279> leaving <179>
R2C3 is the only square in row 2 that can be <2>
Squares R3C3 and R9C5 form a remote naked pair. <69> can be removed from any square that is common to their groups.
R3C5 - removing <69> from <269> leaving <2>
R3C8 can only be <6>
R3C3 can only be <9>
R1C8 can only be <2>
R8C3 can only be <6>
R2C1 can only be <6>
R8C4 can only be <2>
R9C2 can only be <9>
R8C6 can only be <9>
R6C4 can only be <7>
R9C5 can only be <6>
R4C2 can only be <2>
R1C5 can only be <9>
R1C9 can only be <1>
R1C6 can only be <5>
R2C9 can only be <9>
R6C1 can only be <3>
R4C6 can only be <3>
R6C2 can only be <6>
R4C1 can only be <9>
R6C6 can only be <2>
R2C4 can only be <1>
R1C4 can only be <6>
R9C6 can only be <1>
R2C6 can only be <7>
R9C4 can only be <5>
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