Dec 16 - Very Hard
Puzzle Copyright © Kevin Stone
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Reasoning
R3C4 is the only square in row 3 that can be <3>
R5C7 is the only square in row 5 that can be <3>
R6C4 is the only square in row 6 that can be <9>
R7C6 is the only square in row 7 that can be <3>
R7C9 is the only square in row 7 that can be <5>
R7C5 is the only square in row 7 that can be <6>
R3C3 is the only square in row 3 that can be <6>
R9C9 is the only square in row 9 that can be <6>
Squares R7C2 and R8C2 in column 2 form a simple naked pair. These 2 squares both contain the 2 possibilities <27>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the column.
R2C2 - removing <27> from <2578> leaving <58>
R4C2 - removing <7> from <5678> leaving <568>
R6C2 - removing <7> from <67> leaving <6>
R4C8 is the only square in column 8 that can be <6>
Squares R7C2 and R8C2 in block 7 form a simple naked pair. These 2 squares both contain the 2 possibilities <27>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the block.
R7C1 - removing <7> from <47> leaving <4>
R9C3 - removing <2> from <1249> leaving <149>
R7C7 can only be <2>
R7C2 can only be <7>
R8C2 can only be <2>
R8C5 can only be <9>
R9C6 is the only square in row 9 that can be <2>
Squares R3C5 and R3C8 in row 3 form a simple naked pair. These 2 squares both contain the 2 possibilities <12>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the row.
R3C9 - removing <12> from <1279> leaving <79>
Squares R9C1 and R9C3 in row 9 form a simple naked pair. These 2 squares both contain the 2 possibilities <19>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the row.
R9C7 - removing <1> from <148> leaving <48>
Squares R2C5 and R3C5 in block 2 form a simple naked pair. These 2 squares both contain the 2 possibilities <12>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the block.
R2C6 - removing <1> from <179> leaving <79>
Intersection of column 9 with block 6. The value <1> only appears in one or more of squares R4C9, R5C9 and R6C9 of column 9. These squares are the ones that intersect with block 6. Thus, the other (non-intersecting) squares of block 6 cannot contain this value.
R6C7 - removing <1> from <147> leaving <47>
R6C8 - removing <1> from <124> leaving <24>
R8C7 is the only square in column 7 that can be <1>
Squares R4C3<147>, R5C3<14> and R6C1<17> in block 4 form a comprehensive naked triplet. These 3 squares can only contain the 3 possibilities <147>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the block.
R4C1 - removing <17> from <1578> leaving <58>
Squares R1C3<279>, R2C3<279> and R3C1<79> in block 1 form a comprehensive naked triplet. These 3 squares can only contain the 3 possibilities <279>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the block.
R1C1 - removing <79> from <5789> leaving <58>
Squares R3C5, R3C8, R2C5 and R2C8 form a Type-1 Unique Rectangle on <12>.
R2C8 - removing <12> from <128> leaving <8>
R2C2 can only be <5>
R8C8 can only be <4>
R1C7 can only be <7>
R8C6 can only be <7>
R6C8 can only be <2>
R9C7 can only be <8>
R9C4 can only be <4>
R6C7 can only be <4>
R3C9 can only be <9>
R2C4 can only be <7>
R4C2 can only be <8>
R1C1 can only be <8>
R2C6 can only be <9>
R8C4 can only be <8>
R2C3 can only be <2>
R1C6 can only be <6>
R3C1 can only be <7>
R1C9 can only be <2>
R4C1 can only be <5>
R3C8 can only be <1>
R5C4 can only be <6>
R1C4 can only be <5>
R1C3 can only be <9>
R2C5 can only be <1>
R3C5 can only be <2>
R6C1 can only be <1>
R6C9 can only be <7>
R9C1 can only be <9>
R5C3 can only be <4>
R4C9 can only be <1>
R9C3 can only be <1>
R4C6 can only be <4>
R5C6 can only be <1>
R4C3 can only be <7>
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