Sep 12 - Very Hard
Puzzle Copyright © Kevin Stone
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Reasoning
R1C7 is the only square in row 1 that can be <7>
R2C3 is the only square in row 2 that can be <9>
R3C8 is the only square in row 3 that can be <5>
R1C4 is the only square in row 1 that can be <5>
R3C6 is the only square in row 3 that can be <9>
R4C2 is the only square in row 4 that can be <8>
R6C8 is the only square in row 6 that can be <9>
R6C4 is the only square in row 6 that can be <4>
R4C8 is the only square in row 4 that can be <4>
R6C6 is the only square in row 6 that can be <6>
R8C6 is the only square in row 8 that can be <2>
R4C4 is the only square in row 4 that can be <2>
R5C2 is the only square in row 5 that can be <2>
R5C3 is the only square in row 5 that can be <5>
R5C6 is the only square in row 5 that can be <7>
R4C9 is the only square in row 4 that can be <7>
R8C2 is the only square in row 8 that can be <5>
R9C2 is the only square in row 9 that can be <9>
R7C7 is the only square in row 7 that can be <9>
R9C5 is the only square in row 9 that can be <4>
R7C2 is the only square in row 7 that can be <4>
R9C3 is the only square in row 9 that can be <7>
R6C1 is the only square in row 6 that can be <7>
R7C5 is the only square in row 7 that can be <7>
R5C7 is the only square in column 7 that can be <6>
Squares R1C5 and R3C5 in block 2 form a simple naked pair. These 2 squares both contain the 2 possibilities <36>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the block.
R1C6 - removing <3> from <138> leaving <18>
R2C4 - removing <3> from <138> leaving <18>
Intersection of row 2 with block 3. The value <3> 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.
R1C8 - removing <3> from <1238> leaving <128>
R3C9 - removing <3> from <123> leaving <12>
Intersection of row 3 with block 1. The value <8> only appears in one or more of squares R3C1, R3C2 and R3C3 of row 3. These squares are the ones that intersect with block 1. Thus, the other (non-intersecting) squares of block 1 cannot contain this value.
R1C1 - removing <8> from <238> leaving <23>
Intersection of column 9 with block 9. The value <3> only appears in one or more of squares R7C9, R8C9 and R9C9 of column 9. These squares are the ones that intersect with block 9. Thus, the other (non-intersecting) squares of block 9 cannot contain this value.
R7C8 - removing <3> from <1368> leaving <168>
R8C7 - removing <3> from <38> leaving <8>
R9C8 - removing <3> from <2368> leaving <268>
R8C3 can only be <3>
R6C3 can only be <1>
R7C1 can only be <8>
R6C2 can only be <3>
R3C3 can only be <8>
Squares R2C7 and R5C4 form a remote naked pair. <13> can be removed from any square that is common to their groups.
R2C4 - removing <1> from <18> leaving <8>
R1C6 can only be <1>
R1C2 can only be <6>
R4C6 can only be <3>
R4C7 can only be <1>
R9C6 can only be <8>
R5C4 can only be <1>
R2C7 can only be <3>
R5C8 can only be <3>
R2C8 can only be <1>
R1C5 can only be <3>
R3C2 can only be <1>
R1C1 can only be <2>
R3C5 can only be <6>
R7C8 can only be <6>
R3C9 can only be <2>
R3C1 can only be <3>
R9C9 can only be <3>
R1C8 can only be <8>
R7C4 can only be <3>
R9C8 can only be <2>
R9C4 can only be <6>
R7C9 can only be <1>
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