Oct 05 - Very Hard
Puzzle Copyright © Kevin Stone
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Reasoning
R1C4 can only be <5>
R1C6 can only be <1>
R3C5 can only be <3>
R2C5 can only be <2>
R5C7 is the only square in row 5 that can be <2>
R5C2 is the only square in row 5 that can be <5>
Squares R1C7 and R9C7 in column 7 form a simple naked pair. These 2 squares both contain the 2 possibilities <38>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the column.
R3C7 - removing <8> from <158> leaving <15>
R7C7 - removing <38> from <1358> leaving <15>
Squares R8C2<68>, R8C5<58> and R8C9<568> in row 8 form a comprehensive naked triplet. These 3 squares can only contain the 3 possibilities <568>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the row.
R8C1 - removing <68> from <1468> leaving <14>
R8C8 - removing <68> from <1468> leaving <14>
Intersection of column 1 with block 4. The value <6> 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 <6> from <468> leaving <48>
Squares R2C1 and R2C8 in row 2 and R8C1 and R8C8 in row 8 form a Simple X-Wing pattern on possibility <1>. All other instances of this possibility in columns 1 and 8 can be removed.
R3C1 - removing <1> from <189> leaving <89>
R7C1 - removing <1> from <178> leaving <78>
Squares R5C6 and R9C6 in column 6, R1C7 and R9C7 in column 7 and R1C8, R5C8 and R9C8 in column 8 form a Swordfish pattern on possibility <8>. All other instances of this possibility in rows 1, 5 and 9 can be removed.
R1C2 - removing <8> from <3678> leaving <367>
R9C2 - removing <8> from <3678> leaving <367>
R1C3 - removing <8> from <368> leaving <36>
R5C3 - removing <8> from <48> leaving <4>
R9C3 - removing <8> from <3468> leaving <346>
R5C5 - removing <8> from <4678> leaving <467>
R4C5 is the only square in row 4 that can be <4>
R9C8 is the only square in row 9 that can be <4>
R8C8 can only be <1>
R8C1 can only be <4>
R2C8 can only be <7>
R7C7 can only be <5>
R2C2 can only be <3>
R1C8 can only be <8>
R3C7 can only be <1>
R1C7 can only be <3>
R5C8 can only be <6>
R2C9 can only be <9>
R1C3 can only be <6>
R2C1 can only be <1>
R3C9 can only be <5>
R3C3 can only be <8>
R5C5 can only be <7>
R4C9 can only be <8>
R1C2 can only be <7>
R9C3 can only be <3>
R9C7 can only be <8>
R3C1 can only be <9>
R4C1 can only be <6>
R6C9 can only be <7>
R7C9 can only be <3>
R8C9 can only be <6>
R5C4 can only be <9>
R7C5 can only be <8>
R7C1 can only be <7>
R6C5 can only be <6>
R8C5 can only be <5>
R9C6 can only be <9>
R7C3 can only be <1>
R8C2 can only be <8>
R9C4 can only be <7>
R5C6 can only be <8>
R9C2 can only be <6>
R6C1 can only be <8>
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