Apr 13 - Very Hard
Puzzle Copyright © Kevin Stone
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Reasoning
R2C8 can only be <8>
R3C8 can only be <7>
R5C1 can only be <7>
R3C1 is the only square in row 3 that can be <4>
R5C3 is the only square in row 5 that can be <9>
R6C3 is the only square in row 6 that can be <4>
R7C1 is the only square in row 7 that can be <1>
R7C5 is the only square in row 7 that can be <4>
R8C7 is the only square in row 8 that can be <4>
R8C3 is the only square in row 8 that can be <5>
R4C3 is the only square in block 4 that can be <2>
R4C6 can only be <1>
Squares R5C5 and R6C6 in block 5 form a simple naked pair. These 2 squares both contain the 2 possibilities <28>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the block.
R6C4 - removing <28> from <2678> leaving <67>
Squares R7C8 and R8C8 in block 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 block.
R7C9 - removing <3> from <356> leaving <56>
R9C7 - removing <2> from <256> leaving <56>
Intersection of row 2 with block 1. The value <3> only appears in one or more of squares R2C1, R2C2 and R2C3 of row 2. 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 <136> leaving <16>
Intersection of row 9 with block 8. The values <28> only appears in one or more of squares R9C4, R9C5 and R9C6 of row 9. These squares are the ones that intersect with block 8. Thus, the other (non-intersecting) squares of block 8 cannot contain these values.
R7C4 - removing <2> from <259> leaving <59>
R7C6 - removing <2> from <2359> leaving <359>
Squares R8C2, R8C8, R7C2 and R7C8 form a Type-1 Unique Rectangle on <23>.
R7C2 - removing <23> from <236> leaving <6>
R7C9 can only be <5>
R3C2 can only be <9>
R9C3 can only be <3>
R7C4 can only be <9>
R4C9 can only be <3>
R9C7 can only be <6>
R2C3 can only be <1>
R8C2 can only be <2>
R2C7 can only be <9>
R1C3 can only be <6>
R2C2 can only be <3>
R1C7 can only be <1>
R4C1 can only be <6>
R6C9 can only be <8>
R6C6 can only be <2>
R5C9 can only be <1>
R7C6 can only be <3>
R1C4 can only be <8>
R7C8 can only be <2>
R8C8 can only be <3>
R1C6 can only be <9>
R1C5 can only be <3>
R5C7 can only be <2>
R3C9 can only be <6>
R4C4 can only be <7>
R6C1 can only be <3>
R4C7 can only be <5>
R6C4 can only be <6>
R5C5 can only be <8>
R6C7 can only be <7>
R3C6 can only be <5>
R3C4 can only be <2>
R9C6 can only be <8>
R9C5 can only be <2>
R9C4 can only be <5>
R3C5 can only be <1>
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