Oct 13 - Very Hard
Puzzle Copyright © Kevin Stone
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Reasoning
R2C8 can only be <3>
R5C5 can only be <4>
R2C2 can only be <9>
R8C8 can only be <5>
R7C9 can only be <3>
R9C7 can only be <8>
Squares R7C1 and R7C6 in row 7 form a simple naked pair. These 2 squares both contain the 2 possibilities <45>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the row.
R7C4 - removing <4> from <148> leaving <18>
R7C5 - removing <5> from <158> leaving <18>
Squares R9C3 and R9C5 in row 9 form a simple naked pair. These 2 squares both contain the 2 possibilities <35>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the row.
R9C6 - removing <35> from <3567> leaving <67>
Squares R1C3 and R9C3 in column 3 form a simple naked pair. These 2 squares both contain the 2 possibilities <35>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the column.
R4C3 - removing <5> from <2589> leaving <289>
R5C3 - removing <35> from <358> leaving <8>
R6C3 - removing <3> from <239> leaving <29>
R5C8 can only be <1>
R6C8 can only be <2>
R6C3 can only be <9>
R4C8 can only be <8>
R4C3 can only be <2>
R6C1 is the only square in row 6 that can be <1>
Intersection of column 2 with block 4. The values <56> only appears in one or more of squares R4C2, R5C2 and R6C2 of column 2. These squares are the ones that intersect with block 4. Thus, the other (non-intersecting) squares of block 4 cannot contain these values.
R4C1 - removing <5> from <457> leaving <47>
R5C1 - removing <5> from <357> leaving <37>
Squares R5C1 and R5C7 in row 5 form a simple naked pair. These 2 squares both contain the 2 possibilities <37>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the row.
R5C2 - removing <3> from <356> leaving <56>
Squares R3C1 and R9C5 form a remote naked pair. <35> can be removed from any square that is common to their groups.
R3C5 - removing <35> from <359> leaving <9>
R3C9 can only be <4>
R3C4 can only be <6>
R6C9 can only be <6>
R1C7 can only be <9>
R5C9 can only be <5>
R9C4 can only be <7>
R5C2 can only be <6>
R4C9 can only be <9>
R9C6 can only be <6>
R2C4 can only be <1>
R2C5 can only be <2>
R7C4 can only be <8>
R2C6 can only be <7>
R8C5 can only be <3>
R7C5 can only be <1>
R1C4 can only be <4>
R8C2 can only be <4>
R9C5 can only be <5>
R9C3 can only be <3>
R1C5 can only be <8>
R7C6 can only be <4>
R8C4 can only be <9>
R7C1 can only be <5>
R8C6 can only be <2>
R4C2 can only be <5>
R6C2 can only be <3>
R1C3 can only be <5>
R1C6 can only be <3>
R3C1 can only be <3>
R3C6 can only be <5>
R5C1 can only be <7>
R5C7 can only be <3>
R4C1 can only be <4>
R6C7 can only be <4>
R4C7 can only be <7>
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