Jan 28 - Hard
Puzzle Copyright © Kevin Stone
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Reasoning
R7C5 can only be <5>
R8C5 can only be <2>
R2C4 is the only square in row 2 that can be <2>
R2C9 is the only square in row 2 that can be <4>
R3C3 is the only square in row 3 that can be <2>
R3C6 is the only square in row 3 that can be <4>
R5C1 is the only square in row 5 that can be <8>
R1C6 is the only square in row 1 that can be <8>
R2C2 is the only square in row 2 that can be <8>
R7C1 is the only square in row 7 that can be <4>
R7C2 is the only square in row 7 that can be <9>
R8C9 is the only square in row 8 that can be <8>
R9C4 is the only square in row 9 that can be <8>
R8C1 is the only square in column 1 that can be <3>
R8C6 can only be <1>
R7C6 can only be <3>
R7C4 can only be <6>
R3C4 is the only square in block 2 that can be <5>
R5C4 can only be <1>
R4C4 can only be <7>
R8C3 is the only square in block 7 that can be <7>
Squares R7C7 and R7C9 in block 9 form a simple naked pair. These 2 squares both contain the 2 possibilities <17>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the block.
R9C7 - removing <1> from <135> leaving <35>
R9C9 - removing <1> from <1356> leaving <356>
Intersection of column 1 with block 4. The value <5> 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.
R4C2 - removing <5> from <156> leaving <16>
Intersection of block 1 with column 1. The values <17> only appears in one or more of squares R1C1, R2C1 and R3C1 of block 1. These squares are the ones that intersect with column 1. Thus, the other (non-intersecting) squares of column 1 cannot contain these values.
R4C1 - removing <1> from <1569> leaving <569>
R6C1 - removing <1> from <159> leaving <59>
Squares R6C1 and R6C6 in row 6 form a simple naked pair. These 2 squares both contain the 2 possibilities <59>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the row.
R6C3 - removing <9> from <19> leaving <1>
R6C8 - removing <5> from <1357> leaving <137>
R6C9 - removing <59> from <13579> leaving <137>
R9C3 can only be <6>
R4C2 can only be <6>
R1C3 can only be <9>
R8C2 can only be <5>
R8C8 can only be <6>
R9C2 can only be <1>
R1C1 is the only square in row 1 that can be <6>
R3C9 is the only square in row 3 that can be <6>
R3C5 is the only square in row 3 that can be <9>
R2C5 can only be <7>
R2C1 can only be <1>
R2C8 can only be <3>
R3C1 can only be <7>
R2C7 can only be <9>
R6C8 can only be <7>
R3C8 can only be <1>
R6C9 can only be <3>
R1C8 can only be <5>
R9C9 can only be <5>
R9C7 can only be <3>
R5C9 can only be <9>
R1C7 can only be <7>
R5C6 can only be <5>
R4C9 can only be <1>
R7C7 can only be <1>
R4C7 can only be <5>
R7C9 can only be <7>
R6C6 can only be <9>
R6C1 can only be <5>
R4C1 can only be <9>
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