May 30 - Very Hard
Puzzle Copyright © Kevin Stone
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Reasoning
R2C4 can only be <5>
R3C7 can only be <3>
R2C6 can only be <2>
R1C5 can only be <4>
R3C5 can only be <7>
R2C2 is the only square in row 2 that can be <1>
R2C1 is the only square in row 2 that can be <3>
R6C5 is the only square in row 6 that can be <3>
R8C2 is the only square in row 8 that can be <3>
R9C7 is the only square in row 9 that can be <4>
R9C8 is the only square in row 9 that can be <1>
R4C5 is the only square in row 4 that can be <1>
R4C2 is the only square in row 4 that can be <2>
R5C7 is the only square in row 5 that can be <1>
R5C5 is the only square in row 5 that can be <2>
R5C6 is the only square in row 5 that can be <5>
R9C3 is the only square in row 9 that can be <7>
R5C1 is the only square in column 1 that can be <4>
R7C3 is the only square in column 3 that can be <6>
R7C7 can only be <9>
R1C7 can only be <6>
Squares R2C8 and R4C8 in column 8 form a simple naked pair. These 2 squares both contain the 2 possibilities <89>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the column.
R1C8 - removing <9> from <259> leaving <25>
R6C8 - removing <89> from <689> leaving <6>
R5C4 is the only square in row 5 that can be <6>
R8C9 is the only square in row 8 that can be <6>
Squares R2C9 and R5C9 in column 9 form a simple naked pair. These 2 squares both contain the 2 possibilities <89>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the column.
R3C9 - removing <8> from <258> leaving <25>
Intersection of column 3 with block 1. The value <2> only appears in one or more of squares R1C3, R2C3 and R3C3 of column 3. These squares are the ones that intersect with block 1. Thus, the other (non-intersecting) squares of block 1 cannot contain this value.
R3C1 - removing <2> from <258> leaving <58>
Squares R3C9 and R8C1 form a remote naked pair. <25> can be removed from any square that is common to their groups.
R3C1 - removing <5> from <58> leaving <8>
R3C3 can only be <2>
R3C9 can only be <5>
R1C3 can only be <9>
R7C9 can only be <2>
R1C8 can only be <2>
R7C1 can only be <5>
R8C8 can only be <5>
R8C1 can only be <2>
R1C2 can only be <5>
R5C3 can only be <8>
R5C9 can only be <9>
R6C2 can only be <9>
R2C9 can only be <8>
R4C8 can only be <8>
R6C6 can only be <7>
R6C4 can only be <8>
R8C6 can only be <4>
R7C5 can only be <8>
R9C2 can only be <8>
R9C5 can only be <5>
R8C4 can only be <7>
R4C6 can only be <9>
R2C8 can only be <9>
R4C4 can only be <4>
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