Dec 28 - Very Hard
Puzzle Copyright © Kevin Stone
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Reasoning
R4C3 is the only square in row 4 that can be <4>
R4C2 is the only square in row 4 that can be <6>
R5C9 is the only square in row 5 that can be <9>
R7C2 is the only square in row 7 that can be <8>
R3C2 is the only square in column 2 that can be <9>
R5C6 is the only square in column 6 that can be <8>
R7C8 is the only square in column 8 that can be <3>
R7C9 is the only square in row 7 that can be <5>
R7C6 is the only square in row 7 that can be <7>
R1C5 is the only square in column 5 that can be <7>
R1C9 is the only square in row 1 that can be <6>
R3C4 is the only square in row 3 that can be <6>
R3C6 is the only square in row 3 that can be <4>
R8C6 can only be <3>
R2C6 can only be <2>
R8C5 is the only square in row 8 that can be <6>
R6C8 is the only square in column 8 that can be <8>
Squares R2C4 and R2C5 in row 2 form a simple naked pair. These 2 squares both contain the 2 possibilities <39>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the row.
R2C3 - removing <3> from <358> leaving <58>
Squares R8C3 and R9C3 in column 3 form a simple naked pair. These 2 squares both contain the 2 possibilities <29>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the column.
R1C3 - removing <2> from <238> leaving <38>
R6C3 - removing <2> from <235> leaving <35>
Squares R5C2 and R6C2 in block 4 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.
R5C1 - removing <12> from <1235> leaving <35>
Squares R8C3 and R9C3 in block 7 form a simple naked pair. These 2 squares both contain the 2 possibilities <29>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the block.
R9C1 - removing <2> from <124> leaving <14>
Squares R3C1 and R3C8 in row 3 and R5C1 and R5C8 in row 5 form a Simple X-Wing pattern on possibility <5>. All other instances of this possibility in columns 1 and 8 can be removed.
R4C8 - removing <5> from <57> leaving <7>
R3C9 is the only square in row 3 that can be <7>
R9C9 can only be <2>
R9C3 can only be <9>
R8C7 can only be <4>
R8C4 can only be <9>
R9C7 can only be <7>
R9C5 can only be <1>
R8C3 can only be <2>
R9C1 can only be <4>
R4C5 can only be <5>
R7C4 can only be <4>
R4C7 can only be <1>
R6C5 can only be <3>
R6C3 can only be <5>
R2C5 can only be <9>
R5C4 can only be <1>
R7C1 can only be <1>
R2C4 can only be <3>
R5C2 can only be <2>
R6C7 can only be <2>
R2C3 can only be <8>
R5C1 can only be <3>
R6C2 can only be <1>
R1C7 can only be <8>
R5C8 can only be <5>
R1C3 can only be <3>
R2C7 can only be <5>
R3C8 can only be <2>
R3C1 can only be <5>
R1C1 can only be <2>
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