May 10 - Very Hard
Puzzle Copyright © Kevin Stone
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Reasoning
R8C4 can only be <1>
R1C2 is the only square in row 1 that can be <2>
R1C5 is the only square in row 1 that can be <9>
R2C9 is the only square in row 2 that can be <5>
R3C1 is the only square in row 3 that can be <1>
R5C3 is the only square in row 5 that can be <1>
R6C6 is the only square in row 6 that can be <1>
R8C1 is the only square in row 8 that can be <4>
R4C2 is the only square in column 2 that can be <4>
R4C7 is the only square in row 4 that can be <9>
R6C2 is the only square in row 6 that can be <9>
R9C2 can only be <3>
R3C4 is the only square in column 4 that can be <4>
R2C6 is the only square in column 6 that can be <2>
R6C4 is the only square in column 4 that can be <2>
R6C7 can only be <7>
Squares R5C1 and R5C5 in row 5 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 row.
R5C9 - removing <6> from <246> leaving <24>
Squares R4C8 and R6C8 in column 8 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.
R1C8 - removing <3> from <137> leaving <17>
R9C8 - removing <6> from <167> leaving <17>
Intersection of column 1 with block 1. The value <3> only appears in one or more of squares R1C1, R2C1 and R3C1 of column 1. These squares are the ones that intersect with block 1. Thus, the other (non-intersecting) squares of block 1 cannot contain this value.
R1C3 - removing <3> from <378> leaving <78>
Squares R6C3, R6C8, R4C3 and R4C8 form a Type-1 Unique Rectangle on <36>.
R4C3 - removing <36> from <367> leaving <7>
R4C4 can only be <8>
R1C3 can only be <8>
R5C1 can only be <6>
R4C6 can only be <6>
R4C8 can only be <3>
R8C6 can only be <9>
R5C5 can only be <7>
R6C8 can only be <6>
R6C3 can only be <3>
R8C9 can only be <6>
R9C3 can only be <6>
R9C5 can only be <8>
R9C1 can only be <9>
R3C5 can only be <3>
R7C6 can only be <7>
R3C9 can only be <7>
R7C5 can only be <6>
R2C4 can only be <7>
R3C6 can only be <8>
R7C9 can only be <9>
R1C8 can only be <1>
R7C4 can only be <3>
R7C1 can only be <8>
R9C9 can only be <2>
R9C7 can only be <1>
R5C9 can only be <4>
R1C7 can only be <4>
R9C8 can only be <7>
R2C1 can only be <3>
R5C7 can only be <2>
R1C9 can only be <3>
R1C1 can only be <7>
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