Jan 21 - Hard
Puzzle Copyright © Kevin Stone
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Reasoning
R1C7 is the only square in row 1 that can be <4>
R2C6 is the only square in row 2 that can be <8>
R2C4 is the only square in row 2 that can be <3>
R2C8 is the only square in row 2 that can be <6>
R1C5 is the only square in row 1 that can be <6>
R3C5 is the only square in row 3 that can be <2>
R1C6 can only be <7>
R1C8 can only be <9>
R8C6 can only be <2>
R1C1 can only be <1>
R3C7 can only be <5>
R3C8 can only be <7>
R3C1 can only be <9>
R2C9 can only be <1>
R8C8 can only be <5>
R1C3 can only be <2>
R7C9 is the only square in row 7 that can be <2>
R9C7 is the only square in row 9 that can be <8>
R4C7 can only be <1>
R5C7 can only be <9>
R6C4 is the only square in row 6 that can be <9>
R5C4 is the only square in column 4 that can be <2>
Squares R2C2 and R7C2 in column 2 form a simple naked pair. These 2 squares both contain the 2 possibilities <57>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the column.
R4C2 - removing <5> from <245> leaving <24>
R5C2 - removing <57> from <14567> leaving <146>
R6C2 - removing <5> from <1245> leaving <124>
R8C2 - removing <7> from <1679> leaving <169>
R9C2 - removing <7> from <1679> leaving <169>
Squares R4C6 and R5C6 in block 5 form a simple naked pair. These 2 squares both contain the 2 possibilities <34>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the block.
R4C5 - removing <3> from <358> leaving <58>
R5C5 - removing <3> from <1358> leaving <158>
R6C5 - removing <3> from <135> leaving <15>
Squares R8C4 and R9C4 in block 8 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.
R9C5 - removing <1> from <137> leaving <37>
Intersection of column 1 with block 4. The value <3> only appears in one or more of squares R4C1, R5C1 and R6C1 of column 1. These squares are the ones that intersect with block 4. Thus, the other (non-intersecting) squares of block 4 cannot contain this value.
R5C3 - removing <3> from <1357> leaving <157>
R6C3 - removing <3> from <135> leaving <15>
R6C8 is the only square in row 6 that can be <3>
R5C8 can only be <8>
R4C8 can only be <2>
R4C2 can only be <4>
R4C6 can only be <3>
R4C1 can only be <5>
R5C6 can only be <4>
R5C9 can only be <5>
R5C5 can only be <1>
R6C9 can only be <4>
R4C5 can only be <8>
R2C1 can only be <7>
R6C3 can only be <1>
R5C2 can only be <6>
R5C3 can only be <7>
R6C5 can only be <5>
R6C2 can only be <2>
R2C2 can only be <5>
R8C1 can only be <6>
R7C2 can only be <7>
R5C1 can only be <3>
R9C3 can only be <3>
R7C5 can only be <3>
R7C3 can only be <5>
R9C5 can only be <7>
R8C4 can only be <1>
R8C2 can only be <9>
R9C4 can only be <6>
R9C9 can only be <9>
R9C2 can only be <1>
R8C9 can only be <7>
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