Nov 21 - Very Hard

Puzzle Copyright © Kevin Stone

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## Reasoning

R2C2 can only be <3>

R2C8 can only be <9>

R7C1 can only be <8>

R8C2 can only be <2>

R9C7 can only be <6>

R2C5 can only be <5>

R8C8 can only be <7>

R5C2 can only be <7>

R9C3 can only be <5>

R8C5 can only be <9>

R5C8 can only be <8>

R9C4 can only be <2>

R9C6 can only be <8>

R7C9 can only be <9>

R9C5 can only be <4>

R3C5 is the only square in row 3 that can be <8>

R5C1 is the only square in row 5 that can be <5>

R6C3 is the only square in row 6 that can be <8>

R4C1 is the only square in column 1 that can be <3>

Squares R6C1 and R6C7 in row 6 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 row.

R6C5 - removing <2> from <267> leaving <67>

R6C9 - removing <2> from <267> leaving <67>

Intersection of block 5 with column 5. The values <27> only appears in one or more of squares R4C5, R5C5 and R6C5 of block 5. These squares are the ones that intersect with column 5. Thus, the other (non-intersecting) squares of column 5 cannot contain these values.

R1C5 - removing <7> from <137> leaving <13>

R7C5 - removing <7> from <367> leaving <36>

Squares R5C4<36>, R5C5<1236>, R5C6<136> and R5C9<126> in row 5 form a comprehensive naked quad. These 4 squares can only contain the 4 possibilities <1236>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the row.

R5C3 - removing <2> from <249> leaving <49>

R5C7 - removing <12> from <1249> leaving <49>

Squares R1C3 and R6C7 form a remote naked pair. <29> can be removed from any square that is common to their groups.

R1C7 - removing <2> from <12> leaving <1>

R1C5 can only be <3>

R3C9 can only be <2>

R3C1 can only be <9>

R1C6 can only be <7>

R7C5 can only be <6>

R1C4 can only be <9>

R3C4 can only be <6>

R6C1 can only be <2>

R1C3 can only be <2>

R3C6 can only be <1>

R5C4 can only be <3>

R5C6 can only be <6>

R7C4 can only be <7>

R5C9 can only be <1>

R7C6 can only be <3>

R6C5 can only be <7>

R5C5 can only be <2>

R4C9 can only be <7>

R6C7 can only be <9>

R4C3 can only be <4>

R6C9 can only be <6>

R5C7 can only be <4>

R4C7 can only be <2>

R5C3 can only be <9>

R4C5 can only be <1>

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