Aug 18 - Very Hard

Puzzle Copyright © Kevin Stone

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## Reasoning

R9C3 can only be <6>

R3C2 is the only square in row 3 that can be <1>

R3C3 is the only square in row 3 that can be <4>

R3C8 is the only square in row 3 that can be <7>

R4C5 is the only square in row 4 that can be <3>

R5C5 is the only square in row 5 that can be <4>

R1C3 is the only square in column 3 that can be <2>

Intersection of row 7 with block 8. The value <1> only appears in one or more of squares R7C4, R7C5 and R7C6 of row 7. These squares are the ones that intersect with block 8. Thus, the other (non-intersecting) squares of block 8 cannot contain this value.

R8C4 - removing <1> from <1356> leaving <356>

R8C6 - removing <1> from <136> leaving <36>

Intersection of row 9 with block 9. The value <3> only appears in one or more of squares R9C7, R9C8 and R9C9 of row 9. These squares are the ones that intersect with block 9. Thus, the other (non-intersecting) squares of block 9 cannot contain this value.

R8C9 - removing <3> from <136> leaving <16>

Squares R2C6<2369>, R3C4<36>, R3C5<69> and R3C6<2369> in block 2 form a comprehensive naked quad. These 4 squares can only contain the 4 possibilities <2369>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the block.

R1C5 - removing <69> from <5689> leaving <58>

R2C4 - removing <36> from <3568> leaving <58>

Squares R2C4 and R2C9 in row 2, R6C2 and R6C9 in row 6 and R8C2 and R8C4 in row 8 form a Swordfish pattern on possibility <5>. All other instances of this possibility in columns 2, 4 and 9 can be removed.

R1C9 - removing <5> from <569> leaving <69>

R7C2 - removing <5> from <578> leaving <78>

R7C4 - removing <5> from <156> leaving <16>

Squares R1C9 and R4C9 in column 9 form a simple naked pair. These 2 squares both contain the 2 possibilities <69>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the column.

R2C9 - removing <69> from <23569> leaving <235>

R6C9 - removing <6> from <256> leaving <25>

R8C9 - removing <6> from <16> leaving <1>

R9C9 - removing <9> from <139> leaving <13>

R9C9 can only be <3>

R9C7 can only be <9>

R9C5 can only be <7>

R9C1 can only be <1>

R2C6 is the only square in row 2 that can be <3>

R8C6 can only be <6>

R3C4 can only be <6>

R3C5 can only be <9>

R7C4 can only be <1>

R3C6 can only be <2>

R3C7 can only be <3>

R5C4 can only be <8>

R8C8 can only be <8>

R5C6 can only be <1>

R7C6 can only be <9>

R7C5 can only be <5>

R8C1 can only be <4>

R5C3 can only be <5>

R2C4 can only be <5>

R6C5 can only be <6>

R7C3 can only be <8>

R1C5 can only be <8>

R8C4 can only be <3>

R8C2 can only be <5>

R6C1 can only be <8>

R2C9 can only be <2>

R6C9 can only be <5>

R5C7 can only be <6>

R1C7 can only be <5>

R7C7 can only be <2>

R4C9 can only be <9>

R6C2 can only be <4>

R6C8 can only be <2>

R7C8 can only be <6>

R7C2 can only be <7>

R2C8 can only be <9>

R2C1 can only be <6>

R4C8 can only be <4>

R1C9 can only be <6>

R4C2 can only be <6>

R1C1 can only be <9>

R2C2 can only be <8>

R4C1 can only be <7>

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