Jan 20 - Very Hard
Puzzle Copyright © Kevin Stone
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Reasoning
R1C6 is the only square in row 1 that can be <4>
R2C3 is the only square in row 2 that can be <7>
R2C7 is the only square in row 2 that can be <9>
R2C2 is the only square in row 2 that can be <2>
R3C9 is the only square in row 3 that can be <7>
R3C7 is the only square in row 3 that can be <2>
R4C6 is the only square in row 4 that can be <2>
R5C5 is the only square in row 5 that can be <9>
R5C4 is the only square in row 5 that can be <5>
R6C5 is the only square in row 6 that can be <7>
R7C6 is the only square in row 7 that can be <7>
R9C9 is the only square in row 9 that can be <2>
R9C1 is the only square in row 9 that can be <9>
R5C2 is the only square in column 2 that can be <6>
R5C8 is the only square in row 5 that can be <3>
R1C7 is the only square in row 1 that can be <3>
R4C5 is the only square in row 4 that can be <3>
R8C3 is the only square in row 8 that can be <3>
R9C2 can only be <8>
R9C3 can only be <4>
R6C2 can only be <3>
R9C7 can only be <1>
R9C4 can only be <3>
R4C9 is the only square in row 4 that can be <1>
R6C1 is the only square in row 6 that can be <4>
R5C9 is the only square in row 5 that can be <4>
R3C4 is the only square in column 4 that can be <6>
Squares R1C8 and R1C9 in row 1 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.
R1C1 - removing <58> from <1568> leaving <16>
R1C3 - removing <58> from <1568> leaving <16>
Squares R7C1 and R7C3 in row 7 form a simple naked pair. These 2 squares both contain the 2 possibilities <56>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the row.
R7C7 - removing <6> from <468> leaving <48>
Squares R1C1 and R1C3 in block 1 form a simple naked pair. These 2 squares both contain the 2 possibilities <16>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the block.
R2C1 - removing <1> from <158> leaving <58>
Squares R2C4 and R5C1 form a remote naked pair. <18> can be removed from any square that is common to their groups.
R2C1 - removing <8> from <58> leaving <5>
R7C1 can only be <6>
R3C3 can only be <8>
R3C5 can only be <5>
R6C3 can only be <1>
R6C4 can only be <8>
R1C3 can only be <6>
R5C1 can only be <8>
R2C4 can only be <1>
R5C6 can only be <1>
R7C3 can only be <5>
R1C1 can only be <1>
R2C5 can only be <8>
R7C5 can only be <4>
R8C6 can only be <8>
R7C7 can only be <8>
R8C5 can only be <1>
R4C7 can only be <6>
R8C9 can only be <5>
R8C8 can only be <6>
R1C9 can only be <8>
R1C8 can only be <5>
R4C8 can only be <8>
R8C7 can only be <4>
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