Dec 06 - Very Hard
Puzzle Copyright © Kevin Stone
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Reasoning
R5C5 can only be <5>
R3C5 can only be <9>
R2C5 is the only square in row 2 that can be <4>
R5C8 is the only square in row 5 that can be <1>
R5C2 is the only square in row 5 that can be <4>
R8C6 is the only square in row 8 that can be <7>
R2C3 is the only square in column 3 that can be <2>
R2C2 is the only square in row 2 that can be <9>
R1C6 is the only square in column 6 that can be <1>
R4C9 is the only square in column 9 that can be <6>
Squares R8C3 and R8C7 in row 8 form a simple naked pair. These 2 squares both contain the 2 possibilities <89>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the row.
R8C2 - removing <8> from <138> leaving <13>
R8C4 - removing <8> from <238> leaving <23>
R8C8 - removing <8> from <268> leaving <26>
Squares R1C5 and R9C5 in column 5 form a simple naked pair. These 2 squares both contain the 2 possibilities <23>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the column.
R8C5 - removing <23> from <1236> leaving <16>
Squares R8C4 and R9C5 in block 8 form a simple naked pair. These 2 squares both contain the 2 possibilities <23>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the block.
R9C4 - removing <23> from <2358> leaving <58>
Squares R9C4 and R9C6 in row 9 form a simple naked pair. These 2 squares both contain the 2 possibilities <58>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the row.
R9C1 - removing <8> from <389> leaving <39>
R9C9 - removing <8> from <289> leaving <29>
Squares R3C2 and R3C8 in row 3 and R7C2 and R7C8 in row 7 form a Simple X-Wing pattern on possibility <8>. All other instances of this possibility in columns 2 and 8 can be removed.
R2C8 - removing <8> from <3578> leaving <357>
R6C2 - removing <8> from <238> leaving <23>
R6C8 - removing <8> from <238> leaving <23>
Squares R6C2 and R6C8 in row 6 form a simple naked pair. These 2 squares both contain the 2 possibilities <23>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the row.
R6C1 - removing <3> from <389> leaving <89>
R6C9 - removing <23> from <2389> leaving <89>
R9C9 is the only square in column 9 that can be <2>
R9C5 can only be <3>
R8C8 can only be <6>
R8C5 can only be <1>
R7C8 can only be <8>
R9C1 can only be <9>
R1C5 can only be <2>
R8C4 can only be <2>
R7C2 can only be <1>
R3C8 can only be <5>
R8C7 can only be <9>
R8C2 can only be <3>
R7C5 can only be <6>
R8C3 can only be <8>
R6C1 can only be <8>
R3C2 can only be <8>
R6C9 can only be <9>
R1C1 can only be <5>
R5C3 can only be <9>
R6C2 can only be <2>
R4C1 can only be <7>
R4C8 can only be <2>
R5C1 can only be <3>
R4C2 can only be <5>
R6C8 can only be <3>
R5C9 can only be <8>
R5C7 can only be <7>
R1C9 can only be <3>
R2C8 can only be <7>
R1C4 can only be <8>
R2C7 can only be <8>
R9C4 can only be <5>
R2C6 can only be <5>
R2C4 can only be <3>
R9C6 can only be <8>
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