May 21 - Very Hard
Puzzle Copyright © Kevin Stone
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Reasoning
R2C8 can only be <3>
R8C8 can only be <8>
R7C8 can only be <4>
R2C3 is the only square in row 2 that can be <8>
R4C4 is the only square in row 4 that can be <4>
R6C3 is the only square in row 6 that can be <7>
R7C6 is the only square in row 7 that can be <8>
R7C3 is the only square in row 7 that can be <2>
R8C5 is the only square in row 8 that can be <5>
R1C5 can only be <7>
R2C5 can only be <6>
R5C5 can only be <2>
R5C8 can only be <9>
R9C5 can only be <4>
R3C8 can only be <2>
R8C3 is the only square in row 8 that can be <9>
R9C6 is the only square in row 9 that can be <2>
R9C4 is the only square in row 9 that can be <7>
R7C4 can only be <6>
R1C9 is the only square in column 9 that can be <9>
Squares R2C7 and R3C7 in column 7 form a simple naked pair. These 2 squares both contain the 2 possibilities <15>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the column.
R4C7 - removing <5> from <2356> leaving <236>
R6C7 - removing <5> from <256> leaving <26>
Squares R5C9 and R9C9 in column 9 form a simple naked pair. These 2 squares both contain the 2 possibilities <36>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the column.
R4C9 - removing <36> from <3568> leaving <58>
R6C9 - removing <6> from <568> leaving <58>
Intersection of row 1 with block 2. The value <5> only appears in one or more of squares R1C4, R1C5 and R1C6 of row 1. These squares are the ones that intersect with block 2. Thus, the other (non-intersecting) squares of block 2 cannot contain this value.
R3C4 - removing <5> from <359> leaving <39>
R3C6 - removing <5> from <159> leaving <19>
Squares R4C3<36>, R5C1<136> and R5C2<136> in block 4 form a comprehensive naked triplet. These 3 squares can only contain the 3 possibilities <136>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the block.
R4C1 - removing <36> from <2368> leaving <28>
R6C1 - removing <6> from <268> leaving <28>
Squares R5C1 and R9C1 in column 1 and R5C9 and R9C9 in column 9 form a Simple X-Wing pattern on possibility <6>. All other instances of this possibility in rows 5 and 9 can be removed.
R5C2 - removing <6> from <136> leaving <13>
Squares R2C2, R2C7, R3C2 and R3C7 form a Type-1 Unique Rectangle on <15>.
R3C2 - removing <15> from <1356> leaving <36>
R3C7 is the only square in row 3 that can be <5>
R2C7 can only be <1>
R2C2 can only be <5>
R3C6 is the only square in row 3 that can be <1>
R1C6 can only be <5>
R1C4 can only be <3>
R4C6 can only be <6>
R4C3 can only be <3>
R6C6 can only be <9>
R6C4 can only be <5>
R1C1 can only be <1>
R3C4 can only be <9>
R4C7 can only be <2>
R3C3 can only be <6>
R5C2 can only be <1>
R4C1 can only be <8>
R6C7 can only be <6>
R5C1 can only be <6>
R6C9 can only be <8>
R8C7 can only be <7>
R5C9 can only be <3>
R6C1 can only be <2>
R4C9 can only be <5>
R8C2 can only be <6>
R7C7 can only be <3>
R3C2 can only be <3>
R9C1 can only be <3>
R9C9 can only be <6>
R7C2 can only be <7>
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