Aug 13 - Very Hard
Puzzle Copyright © Kevin Stone
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Reasoning
R5C6 can only be <2>
R8C4 can only be <7>
R4C5 can only be <7>
R1C7 is the only square in row 1 that can be <7>
R2C2 is the only square in row 2 that can be <6>
R2C3 is the only square in row 2 that can be <2>
R5C5 is the only square in row 5 that can be <5>
R5C3 is the only square in row 5 that can be <7>
R7C8 is the only square in row 7 that can be <7>
R7C2 is the only square in row 7 that can be <5>
R8C3 is the only square in row 8 that can be <4>
R8C8 is the only square in row 8 that can be <5>
Squares R8C2 and R9C3 in block 7 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 block.
R9C1 - removing <8> from <268> leaving <26>
Intersection of column 8 with block 3. The value <8> only appears in one or more of squares R1C8, R2C8 and R3C8 of column 8. These squares are the ones that intersect with block 3. Thus, the other (non-intersecting) squares of block 3 cannot contain this value.
R2C7 - removing <8> from <189> leaving <19>
Squares R2C6 and R2C7 in row 2 form a simple naked pair. These 2 squares both contain the 2 possibilities <19>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the row.
R2C8 - removing <9> from <389> leaving <38>
Squares R2C6 and R2C7 in row 2 and R8C6 and R8C7 in row 8 form a Simple X-Wing pattern on possibility <9>. All other instances of this possibility in columns 6 and 7 can be removed.
R5C7 - removing <9> from <69> leaving <6>
R9C7 - removing <9> from <1689> leaving <168>
Squares R9C3 and R9C7 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.
R9C5 - removing <1> from <129> leaving <29>
R9C9 - removing <1> from <169> leaving <69>
Squares R3C2 and R4C2 in column 2 and R3C8 and R4C8 in column 8 form a Simple X-Wing pattern on possibility <9>. All other instances of this possibility in rows 3 and 4 can be removed.
R3C1 - removing <9> from <489> leaving <48>
R3C5 - removing <9> from <1389> leaving <138>
R3C9 - removing <9> from <1349> leaving <134>
Squares R2C8 and R6C5 form a remote naked pair. <38> can be removed from any square that is common to their groups.
R6C8 - removing <3> from <23> leaving <2>
R6C2 can only be <8>
R4C8 can only be <9>
R4C2 can only be <2>
R5C9 can only be <3>
R5C4 can only be <8>
R6C5 can only be <3>
R8C2 can only be <1>
R5C1 can only be <9>
R8C6 can only be <9>
R3C2 can only be <9>
R9C3 can only be <8>
R8C7 can only be <8>
R2C6 can only be <1>
R9C5 can only be <2>
R9C7 can only be <1>
R1C3 can only be <1>
R9C1 can only be <6>
R7C5 can only be <1>
R2C7 can only be <9>
R7C9 can only be <6>
R3C5 can only be <8>
R1C9 can only be <4>
R3C1 can only be <4>
R3C8 can only be <3>
R1C5 can only be <9>
R2C4 can only be <3>
R2C8 can only be <8>
R7C1 can only be <2>
R9C9 can only be <9>
R1C1 can only be <8>
R3C9 can only be <1>
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