May 26 - Very Hard
Puzzle Copyright © Kevin Stone
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Reasoning
R6C5 can only be <9>
R4C5 can only be <8>
R7C5 can only be <2>
R5C5 can only be <3>
R3C5 can only be <4>
R6C1 is the only square in row 6 that can be <4>
R9C3 is the only square in row 9 that can be <4>
R2C2 is the only square in row 2 that can be <4>
R9C7 is the only square in row 9 that can be <8>
R5C8 is the only square in row 5 that can be <8>
R5C3 is the only square in column 3 that can be <1>
R7C4 is the only square in column 4 that can be <9>
R1C6 is the only square in column 6 that can be <2>
R7C6 is the only square in block 8 that can be <1>
R8C8 is the only square in column 8 that can be <1>
R8C9 is the only square in row 8 that can be <7>
R1C7 is the only square in column 7 that can be <1>
Squares R9C4 and R9C6 in row 9 form a simple naked pair. These 2 squares both contain the 2 possibilities <35>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the row.
R9C1 - removing <35> from <2356> leaving <26>
R9C9 - removing <5> from <256> leaving <26>
Intersection of row 3 with block 2. The value <3> only appears in one or more of squares R3C4, R3C5 and R3C6 of row 3. These squares are the ones that intersect with block 2. Thus, the other (non-intersecting) squares of block 2 cannot contain this value.
R1C4 - removing <3> from <367> leaving <67>
Intersection of row 5 with block 4. The value <7> only appears in one or more of squares R5C1, R5C2 and R5C3 of row 5. These squares are the ones that intersect with block 4. Thus, the other (non-intersecting) squares of block 4 cannot contain this value.
R4C1 - removing <7> from <679> leaving <69>
Intersection of row 5 with block 6. The value <5> only appears in one or more of squares R5C7, R5C8 and R5C9 of row 5. These squares are the ones that intersect with block 6. Thus, the other (non-intersecting) squares of block 6 cannot contain this value.
R6C9 - removing <5> from <156> leaving <16>
Intersection of column 3 with block 1. The value <6> 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.
R1C1 - removing <6> from <3679> leaving <379>
R2C1 - removing <6> from <3567> leaving <357>
R3C2 - removing <6> from <567> leaving <57>
Squares R3C2 and R3C8 in row 3 and R7C2 and R7C8 in row 7 form a Simple X-Wing pattern on possibility <5>. All other instances of this possibility in columns 2 and 8 can be removed.
R2C8 - removing <5> from <567> leaving <67>
R8C2 - removing <5> from <59> leaving <9>
R8C3 can only be <3>
R2C3 can only be <6>
R2C8 can only be <7>
R1C3 can only be <9>
R5C7 is the only square in column 7 that can be <6>
R5C2 can only be <7>
R6C9 can only be <1>
R4C9 can only be <9>
R4C1 can only be <6>
R5C9 can only be <5>
R5C1 can only be <9>
R3C2 can only be <5>
R3C8 can only be <6>
R7C2 can only be <6>
R2C1 can only be <3>
R7C8 can only be <5>
R1C9 can only be <3>
R4C6 can only be <7>
R9C1 can only be <2>
R4C4 can only be <1>
R3C6 can only be <3>
R8C7 can only be <2>
R8C1 can only be <5>
R2C7 can only be <5>
R9C9 can only be <6>
R1C1 can only be <7>
R2C9 can only be <2>
R3C4 can only be <7>
R9C6 can only be <5>
R9C4 can only be <3>
R6C6 can only be <6>
R1C4 can only be <6>
R6C4 can only be <5>
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