Aug 19 - Very Hard
Puzzle Copyright © Kevin Stone
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Reasoning
R2C8 can only be <4>
R3C4 can only be <2>
R1C2 is the only square in row 1 that can be <5>
R1C3 is the only square in row 1 that can be <4>
R3C8 is the only square in row 3 that can be <1>
R1C6 is the only square in row 1 that can be <1>
R1C5 is the only square in row 1 that can be <7>
R2C5 can only be <8>
R2C1 can only be <2>
R3C5 can only be <9>
R2C3 can only be <7>
R1C1 is the only square in row 1 that can be <9>
R4C1 is the only square in row 4 that can be <1>
R4C8 is the only square in row 4 that can be <5>
R6C2 is the only square in row 6 that can be <8>
R6C4 is the only square in row 6 that can be <4>
R5C2 is the only square in row 5 that can be <4>
R7C9 is the only square in row 7 that can be <8>
R7C8 is the only square in row 7 that can be <6>
R6C9 is the only square in row 6 that can be <6>
R5C1 is the only square in row 5 that can be <6>
R3C2 is the only square in row 3 that can be <6>
Squares R8C5 and R8C9 in row 8 form a simple naked pair. These 2 squares both contain the 2 possibilities <35>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the row.
R8C2 - removing <3> from <379> leaving <79>
R8C7 - removing <3> from <379> leaving <79>
Intersection of row 6 with block 6. The value <3> only appears in one or more of squares R6C7, R6C8 and R6C9 of row 6. These squares are the ones that intersect with block 6. Thus, the other (non-intersecting) squares of block 6 cannot contain this value.
R5C7 - removing <3> from <12379> leaving <1279>
R5C8 - removing <3> from <379> leaving <79>
R5C9 - removing <3> from <123> leaving <12>
Squares R9C1<38>, R9C3<389>, R9C4<37> and R9C8<379> in row 9 form a comprehensive naked quad. These 4 squares can only contain the 4 possibilities <3789>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the row.
R9C5 - removing <3> from <345> leaving <45>
R9C7 - removing <379> from <13479> leaving <14>
R9C9 - removing <3> from <135> leaving <15>
Squares R3C1, R3C3, R9C1 and R9C3 form a Type-1 Unique Rectangle on <38>.
R9C3 - removing <38> from <389> leaving <9>
R8C2 can only be <7>
R8C7 can only be <9>
R7C2 can only be <3>
R4C2 can only be <9>
R9C1 can only be <8>
R3C1 can only be <3>
R3C3 can only be <8>
R5C8 is the only square in row 5 that can be <9>
R6C8 can only be <3>
R6C7 can only be <2>
R9C8 can only be <7>
R9C4 can only be <3>
R7C7 can only be <4>
R6C6 can only be <9>
R1C7 can only be <3>
R5C9 can only be <1>
R7C5 can only be <2>
R9C7 can only be <1>
R4C4 can only be <7>
R8C5 can only be <5>
R9C9 can only be <5>
R5C7 can only be <7>
R9C5 can only be <4>
R8C9 can only be <3>
R1C9 can only be <2>
R4C6 can only be <2>
R4C3 can only be <3>
R7C6 can only be <7>
R5C5 can only be <3>
R5C3 can only be <2>
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