May 19 - Very Hard
Puzzle Copyright © Kevin Stone
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Reasoning
R8C2 can only be <5>
R8C3 can only be <1>
R1C4 is the only square in row 1 that can be <1>
R1C5 is the only square in row 1 that can be <9>
R3C1 is the only square in row 3 that can be <5>
R7C1 is the only square in row 7 that can be <9>
R6C9 is the only square in row 6 that can be <9>
R4C3 is the only square in row 4 that can be <9>
R5C6 is the only square in row 5 that can be <9>
R6C7 is the only square in row 6 that can be <1>
R6C2 is the only square in row 6 that can be <8>
R8C4 is the only square in row 8 that can be <7>
R7C4 is the only square in column 4 that can be <5>
R3C5 is the only square in column 5 that can be <7>
Squares R9C1 and R9C2 in row 9 form a simple naked pair. These 2 squares both contain the 2 possibilities <23>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the row.
R9C5 - removing <2> from <268> leaving <68>
R9C6 - removing <2> from <126> leaving <16>
R9C8 - removing <3> from <3568> leaving <568>
R9C9 - removing <3> from <13568> leaving <1568>
Squares R1C9 and R4C9 in column 9 form a simple naked pair. These 2 squares both contain the 2 possibilities <67>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the column.
R3C9 - removing <6> from <368> leaving <38>
R5C9 - removing <67> from <5678> leaving <58>
R9C9 - removing <6> from <1568> leaving <158>
Intersection of row 1 with block 1. The value <4> only appears in one or more of squares R1C1, R1C2 and R1C3 of row 1. These squares are the ones that intersect with block 1. Thus, the other (non-intersecting) squares of block 1 cannot contain this value.
R3C2 - removing <4> from <246> leaving <26>
Squares R2C3, R3C3 and R5C3 in column 3, R2C4, R3C4 and R5C4 in column 4 and R2C7 and R5C7 in column 7 form a Swordfish pattern on possibility <2>. All other instances of this possibility in rows 2, 3 and 5 can be removed.
R5C1 - removing <2> from <23467> leaving <3467>
R3C2 - removing <2> from <26> leaving <6>
R5C2 - removing <2> from <2346> leaving <346>
R2C6 - removing <2> from <236> leaving <36>
R3C6 - removing <2> from <2346> leaving <346>
R2C8 - removing <2> from <23678> leaving <3678>
R5C8 - removing <2> from <25678> leaving <5678>
R7C6 is the only square in column 6 that can be <2>
R7C9 is the only square in row 7 that can be <1>
R7C8 is the only square in row 7 that can be <3>
R2C6 is the only square in row 2 that can be <3>
R3C6 can only be <4>
R3C4 can only be <2>
R8C6 can only be <6>
R8C7 can only be <4>
R9C6 can only be <1>
R9C5 can only be <8>
R7C7 can only be <8>
R9C9 can only be <5>
R7C5 can only be <4>
R9C8 can only be <6>
R5C9 can only be <8>
R3C3 can only be <8>
R2C4 can only be <6>
R3C9 can only be <3>
R2C7 can only be <2>
R5C4 can only be <4>
R5C7 can only be <6>
R1C8 can only be <7>
R2C3 can only be <7>
R5C2 can only be <3>
R4C9 can only be <7>
R1C9 can only be <6>
R2C8 can only be <8>
R4C8 can only be <2>
R5C8 can only be <5>
R5C3 can only be <2>
R4C5 can only be <6>
R5C1 can only be <7>
R9C2 can only be <2>
R6C1 can only be <6>
R6C5 can only be <2>
R4C1 can only be <4>
R9C1 can only be <3>
R1C2 can only be <4>
R1C1 can only be <2>
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