Sep 25 - Very Hard
Puzzle Copyright © Kevin Stone
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Reasoning
R3C1 is the only square in row 3 that can be <5>
R3C9 is the only square in row 3 that can be <3>
R3C6 is the only square in row 3 that can be <8>
R4C4 is the only square in row 4 that can be <7>
R3C4 can only be <9>
R3C5 can only be <7>
R1C1 is the only square in row 1 that can be <7>
R4C3 is the only square in row 4 that can be <8>
R7C9 is the only square in row 7 that can be <6>
R2C4 is the only square in row 2 that can be <6>
R7C1 is the only square in row 7 that can be <8>
R8C1 can only be <3>
R8C4 can only be <1>
R9C1 can only be <4>
R8C6 can only be <2>
R8C9 can only be <8>
R9C2 can only be <5>
R9C3 can only be <6>
R9C5 can only be <9>
R1C7 is the only square in row 1 that can be <8>
R1C8 is the only square in row 1 that can be <6>
R6C7 is the only square in row 6 that can be <6>
R6C2 is the only square in row 6 that can be <4>
R4C7 is the only square in row 4 that can be <4>
Squares R1C9 and R2C9 in column 9 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 column.
R5C9 - removing <9> from <129> leaving <12>
Intersection of row 5 with block 4. The value <9> only appears in one or more of squares R5C1, R5C2 and R5C3 of row 5. These squares are the ones that intersect with block 4. Thus, the other (non-intersecting) squares of block 4 cannot contain this value.
R6C3 - removing <9> from <359> leaving <35>
Squares R6C3 and R6C4 in row 6 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.
R6C6 - removing <3> from <139> leaving <19>
R6C8 - removing <3> from <139> leaving <19>
Squares R6C6, R6C8, R4C6 and R4C8 form a Type-2 Unique Rectangle on <19>.
R4C2 - removing <3> from <13> leaving <1>
R1C2 can only be <3>
R5C1 can only be <9>
R2C1 can only be <1>
R1C3 can only be <9>
R1C9 can only be <4>
R1C5 can only be <1>
R2C9 can only be <9>
R2C6 can only be <4>
R7C6 can only be <3>
R7C4 can only be <5>
R4C6 can only be <9>
R5C5 can only be <5>
R4C8 can only be <3>
R6C6 can only be <1>
R9C8 can only be <1>
R5C7 can only be <2>
R5C3 can only be <3>
R7C5 can only be <4>
R6C4 can only be <3>
R5C9 can only be <1>
R9C7 can only be <3>
R9C9 can only be <2>
R6C8 can only be <9>
R6C3 can only be <5>
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