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May 30 - Very Hard

## 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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