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Mar 01 - Very Hard

## Reasoning

R2C6 can only be <5>

R4C2 can only be <9>

R4C8 can only be <6>

R5C4 can only be <6>

R5C9 can only be <8>

R6C2 can only be <8>

R6C5 can only be <3>

R7C7 can only be <4>

R8C6 can only be <7>

R5C6 can only be <1>

R1C5 can only be <6>

R4C5 can only be <7>

R5C5 can only be <5>

R2C4 can only be <9>

R5C1 can only be <2>

R6C8 can only be <4>

R9C5 can only be <9>

R8C4 can only be <3>

R2C9 is the only square in row 2 that can be <4>

R8C7 is the only square in row 8 that can be <9>

R8C8 is the only square in row 8 that can be <1>

R9C2 is the only square in row 9 that can be <4>

Squares R3C3 and R3C8 in row 3 form a simple naked pair. These 2 squares both contain the 2 possibilities <58>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the row.

R3C2 - removing <5> from <156> leaving <16>

Intersection of row 9 with block 9. The value <2> only appears in one or more of squares R9C7, R9C8 and R9C9 of row 9. These squares are the ones that intersect with block 9. Thus, the other (non-intersecting) squares of block 9 cannot contain this value.

R8C9 - removing <2> from <25> leaving <5>

Squares R1C9 and R2C8 in block 3 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.

R1C8 - removing <23> from <2358> leaving <58>

Squares R3C2, R3C7, R2C2 and R2C7 form a Type-1 Unique Rectangle on <16>.

R2C2 - removing <16> from <1236> leaving <23>

R2C7 is the only square in row 2 that can be <1>

R3C7 can only be <6>

R3C2 can only be <1>

R2C1 is the only square in row 2 that can be <6>

R8C1 can only be <8>

R8C3 can only be <2>

R1C1 can only be <3>

R8C2 can only be <6>

R2C3 can only be <7>

R1C9 can only be <2>

R9C1 can only be <7>

R2C2 can only be <2>

R1C2 can only be <5>

R9C9 can only be <3>

R2C8 can only be <3>

R7C3 can only be <5>

R7C8 can only be <7>

R7C2 can only be <3>

R3C3 can only be <8>

R9C8 can only be <2>

R1C8 can only be <8>

R3C8 can only be <5>

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