Jan 18 - Very Hard
Puzzle Copyright © Kevin Stone
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Reasoning
R3C4 can only be <5>
R5C5 can only be <5>
R3C6 can only be <8>
R2C6 can only be <6>
R5C1 can only be <7>
R8C5 can only be <4>
R9C5 can only be <8>
R2C4 can only be <9>
R5C2 can only be <1>
R5C9 can only be <8>
R5C8 can only be <9>
R1C1 is the only square in row 1 that can be <6>
R9C1 can only be <5>
R1C3 is the only square in row 1 that can be <5>
R1C7 is the only square in row 1 that can be <9>
R2C8 is the only square in row 2 that can be <8>
R4C8 is the only square in row 4 that can be <6>
R6C3 is the only square in row 6 that can be <8>
R7C6 is the only square in row 7 that can be <1>
R8C6 can only be <5>
R7C8 is the only square in row 7 that can be <5>
R8C8 is the only square in row 8 that can be <2>
R9C9 is the only square in row 9 that can be <6>
R2C7 is the only square in column 7 that can be <4>
R4C3 is the only square in column 3 that can be <4>
Squares R4C2 and R6C2 in column 2 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 column.
R2C2 - removing <3> from <237> leaving <27>
R3C2 - removing <3> from <2347> leaving <247>
R7C2 - removing <3> from <3467> leaving <467>
R8C2 - removing <3> from <367> leaving <67>
Squares R8C2 and R8C4 in row 8 form a simple naked pair. These 2 squares both contain the 2 possibilities <67>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the row.
R8C3 - removing <7> from <137> leaving <13>
R8C7 - removing <7> from <137> leaving <13>
Intersection of row 2 with block 1. The value <7> only appears in one or more of squares R2C1, R2C2 and R2C3 of row 2. These squares are the ones that intersect with block 1. Thus, the other (non-intersecting) squares of block 1 cannot contain this value.
R3C2 - removing <7> from <247> leaving <24>
Squares R4C2, R4C7, R6C2 and R6C7 form a Type-1 Unique Rectangle on <35>.
R6C7 - removing <35> from <357> leaving <7>
R6C8 can only be <3>
R9C7 can only be <1>
R6C2 can only be <5>
R3C8 can only be <7>
R4C7 can only be <5>
R9C3 can only be <7>
R8C7 can only be <3>
R4C2 can only be <3>
R8C3 can only be <1>
R7C9 can only be <7>
R2C3 can only be <3>
R8C2 can only be <6>
R2C5 can only be <2>
R3C1 can only be <4>
R2C2 can only be <7>
R1C5 can only be <3>
R3C2 can only be <2>
R7C1 can only be <3>
R3C9 can only be <3>
R1C9 can only be <2>
R7C4 can only be <6>
R8C4 can only be <7>
R7C2 can only be <4>
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