Jan 10 - Very Hard
Puzzle Copyright © Kevin Stone
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Reasoning
R1C8 can only be <2>
R4C7 can only be <7>
R7C8 can only be <5>
R9C9 can only be <7>
R6C7 can only be <3>
R5C8 can only be <8>
R9C8 can only be <4>
R3C8 can only be <3>
R9C1 can only be <8>
R9C2 can only be <5>
R2C3 is the only square in row 2 that can be <3>
R2C7 is the only square in row 2 that can be <4>
R2C1 is the only square in row 2 that can be <6>
R3C3 is the only square in row 3 that can be <4>
R3C7 is the only square in row 3 that can be <5>
R4C5 is the only square in row 4 that can be <2>
R5C6 is the only square in row 5 that can be <3>
R6C4 is the only square in row 6 that can be <4>
R7C2 is the only square in row 7 that can be <2>
R8C9 is the only square in row 8 that can be <3>
R8C5 is the only square in row 8 that can be <5>
R5C4 is the only square in row 5 that can be <5>
Squares R7C4 and R7C6 in row 7 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.
R7C3 - removing <7> from <179> leaving <19>
Intersection of row 1 with block 1. The value <7> only appears in one or more of squares R1C1, R1C2 and R1C3 of row 1. 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 <179> leaving <19>
Intersection of column 5 with block 5. The value <7> only appears in one or more of squares R4C5, R5C5 and R6C5 of column 5. These squares are the ones that intersect with block 5. Thus, the other (non-intersecting) squares of block 5 cannot contain this value.
R6C6 - removing <7> from <789> leaving <89>
Squares R7C3, R7C7, R8C3 and R8C7 form a Type-1 Unique Rectangle on <19>.
R8C3 - removing <19> from <179> leaving <7>
R8C1 can only be <1>
R6C3 can only be <8>
R6C6 can only be <9>
R4C3 can only be <1>
R6C5 can only be <7>
R3C6 can only be <7>
R8C7 can only be <9>
R1C1 can only be <7>
R7C3 can only be <9>
R7C7 can only be <1>
R3C4 can only be <1>
R7C6 can only be <6>
R4C4 can only be <6>
R5C2 can only be <7>
R4C6 can only be <8>
R7C4 can only be <7>
R5C5 can only be <1>
R2C5 can only be <9>
R2C9 can only be <1>
R1C9 can only be <9>
R3C2 can only be <9>
R1C2 can only be <1>
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