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Jun 13 - Very Hard

Reasoning

R1C4 is the only square in row 1 that can be <7>

R4C4 can only be <4>

R2C8 is the only square in row 2 that can be <8>

R6C6 is the only square in row 6 that can be <8>

R9C1 is the only square in row 9 that can be <8>

Squares R2C2 and R2C5 in row 2 form a simple naked pair. These 2 squares both contain the 2 possibilities <45>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the row.

R2C1 - removing <4> from <134> leaving <13>

R2C9 - removing <45> from <1345> leaving <13>

Squares R7C9<257>, R8C8<24>, R9C7<27> and R9C8<245> in block 9 form a comprehensive naked quad. These 4 squares can only contain the 4 possibilities <2457>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the block.

R8C9 - removing <24> from <2469> leaving <69>

R9C9 - removing <2457> from <245679> leaving <69>

Intersection of column 9 with block 3. The value <4> only appears in one or more of squares R1C9, R2C9 and R3C9 of column 9. These squares are the ones that intersect with block 3. Thus, the other (non-intersecting) squares of block 3 cannot contain this value.

R1C8 - removing <4> from <1245> leaving <125>

Squares R3C5 and R3C9 in row 3 and R7C5 and R7C9 in row 7 form a Simple X-Wing pattern on possibility <5>. All other instances of this possibility in columns 5 and 9 can be removed.

R1C9 - removing <5> from <12345> leaving <1234>

R2C5 - removing <5> from <45> leaving <4>

R6C5 - removing <5> from <579> leaving <79>

R2C2 can only be <5>

R6C4 is the only square in row 6 that can be <5>

R9C4 can only be <9>

R9C9 can only be <6>

R5C4 can only be <1>

R8C9 can only be <9>

R5C8 can only be <2>

R8C8 can only be <4>

R8C2 can only be <6>

R9C8 can only be <5>

R1C8 can only be <1>

R2C9 can only be <3>

R2C1 can only be <1>

R4C9 can only be <7>

R1C7 can only be <2>

R4C1 can only be <6>

R6C9 can only be <1>

R7C9 can only be <2>

R5C7 can only be <3>

R5C6 can only be <6>

R7C1 can only be <7>

R7C5 can only be <5>

R1C9 can only be <4>

R9C7 can only be <7>

R9C2 can only be <4>

R1C2 can only be <9>

R3C9 can only be <5>

R3C5 can only be <6>

R3C1 can only be <4>

R5C3 can only be <4>

R9C3 can only be <3>

R1C6 can only be <5>

R6C1 can only be <9>

R9C6 can only be <2>

R1C3 can only be <6>

R8C1 can only be <2>

R4C6 can only be <3>

R8C5 can only be <3>

R1C1 can only be <3>

R5C2 can only be <7>

R4C5 can only be <2>

R5C5 can only be <9>

R6C5 can only be <7>

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