Jul 27 - Very Hard
Puzzle Copyright © Kevin Stone
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Reasoning
R3C6 is the only square in row 3 that can be <1>
R3C7 is the only square in row 3 that can be <3>
R5C4 is the only square in row 5 that can be <2>
R4C3 is the only square in row 4 that can be <2>
R5C6 is the only square in row 5 that can be <5>
R6C4 is the only square in row 6 that can be <3>
R8C2 is the only square in row 8 that can be <3>
Squares R3C1 and R3C4 in row 3 form a simple naked pair. These 2 squares both contain the 2 possibilities <78>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the row.
R3C3 - removing <78> from <456789> leaving <4569>
Squares R4C6 and R4C7 in row 4 form a simple naked pair. These 2 squares both contain the 2 possibilities <49>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the row.
R4C5 - removing <9> from <689> leaving <68>
Intersection of column 8 with block 3. The value <4> 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 <4> from <245> leaving <25>
Squares R2C2<45>, R2C7<25> and R2C8<24> in row 2 form a comprehensive naked triplet. These 3 squares can only contain the 3 possibilities <245>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the row.
R2C3 - removing <45> from <4578> leaving <78>
Squares R3C1 and R7C1 in column 1 and R3C4 and R7C4 in column 4 form a Simple X-Wing pattern on possibility <7>. All other instances of this possibility in rows 3 and 7 can be removed.
R7C3 - removing <7> from <14578> leaving <1458>
R7C6 - removing <7> from <79> leaving <9>
R7C7 - removing <7> from <125679> leaving <12569>
R7C8 - removing <7> from <2679> leaving <269>
R7C9 can only be <5>
R4C6 can only be <4>
R3C9 can only be <9>
R1C7 can only be <6>
R4C7 can only be <9>
R6C6 can only be <7>
R5C8 can only be <7>
R6C7 can only be <4>
R1C3 can only be <9>
R8C7 can only be <7>
R3C8 can only be <4>
R3C2 can only be <5>
R2C8 can only be <2>
R8C3 can only be <5>
R8C5 can only be <6>
R9C7 can only be <1>
R9C3 can only be <7>
R7C7 can only be <2>
R6C3 can only be <1>
R2C7 can only be <5>
R7C8 can only be <6>
R3C3 can only be <6>
R2C2 can only be <4>
R6C5 can only be <9>
R5C2 can only be <9>
R5C5 can only be <1>
R7C4 can only be <7>
R8C8 can only be <9>
R4C5 can only be <8>
R2C3 can only be <8>
R7C1 can only be <8>
R7C2 can only be <1>
R2C5 can only be <7>
R7C3 can only be <4>
R3C1 can only be <7>
R3C4 can only be <8>
R4C4 can only be <6>
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