Dec 15 - Very Hard
Puzzle Copyright © Kevin Stone
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Reasoning
R5C5 can only be <1>
R7C8 can only be <7>
R5C7 can only be <3>
R5C3 can only be <2>
R8C8 can only be <4>
R4C8 can only be <5>
R6C8 can only be <2>
R3C8 can only be <9>
R7C9 is the only square in row 7 that can be <3>
R9C3 is the only square in row 9 that can be <4>
R9C9 is the only square in row 9 that can be <9>
R1C9 is the only square in column 9 that can be <8>
Squares R4C5 and R6C5 in column 5 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 column.
R1C5 - removing <7> from <2579> leaving <259>
R8C5 - removing <67> from <267> leaving <2>
R9C5 - removing <6> from <2356> leaving <235>
R9C1 is the only square in row 9 that can be <2>
R1C6 is the only square in row 1 that can be <2>
R1C4 is the only square in row 1 that can be <7>
R8C6 is the only square in row 8 that can be <7>
Squares R8C7 and R9C7 in column 7 form a simple naked pair. These 2 squares both contain the 2 possibilities <68>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the column.
R6C7 - removing <6> from <146> leaving <14>
Squares R4C5 and R6C5 in block 5 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 block.
R6C4 - removing <6> from <468> leaving <48>
Intersection of row 7 with block 7. The value <6> only appears in one or more of squares R7C1, R7C2 and R7C3 of row 7. These squares are the ones that intersect with block 7. Thus, the other (non-intersecting) squares of block 7 cannot contain this value.
R8C1 - removing <6> from <16> leaving <1>
R7C6 is the only square in row 7 that can be <1>
Squares R8C4, R8C7, R9C4 and R9C7 form a Type-1 Unique Rectangle on <68>.
R9C4 - removing <68> from <368> leaving <3>
R9C5 can only be <5>
R9C6 can only be <8>
R1C5 can only be <9>
R9C7 can only be <6>
R4C6 can only be <4>
R8C4 can only be <6>
R8C7 can only be <8>
R2C5 can only be <3>
R2C3 can only be <1>
R2C6 can only be <5>
R6C4 can only be <8>
R2C4 can only be <4>
R1C3 can only be <6>
R2C9 can only be <2>
R3C4 can only be <1>
R2C2 can only be <9>
R3C9 can only be <4>
R3C7 can only be <5>
R1C1 can only be <5>
R7C3 can only be <8>
R6C2 can only be <1>
R3C1 can only be <3>
R3C2 can only be <2>
R1C7 can only be <1>
R6C7 can only be <4>
R6C9 can only be <6>
R4C2 can only be <8>
R6C5 can only be <7>
R4C9 can only be <1>
R7C2 can only be <5>
R4C3 can only be <3>
R7C1 can only be <6>
R4C1 can only be <7>
R4C5 can only be <6>
R6C1 can only be <9>
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