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Nov 25 - Very Hard

## Reasoning

R3C7 is the only square in row 3 that can be <4>

R3C2 is the only square in row 3 that can be <9>

R6C3 is the only square in row 6 that can be <8>

R8C4 is the only square in row 8 that can be <4>

R9C9 is the only square in row 9 that can be <4>

R6C1 is the only square in row 6 that can be <4>

R4C8 is the only square in row 4 that can be <4>

R9C1 is the only square in column 1 that can be <6>

R1C1 is the only square in column 1 that can be <2>

R5C3 is the only square in column 3 that can be <9>

R7C4 is the only square in column 4 that can be <6>

R2C7 is the only square in block 3 that can be <6>

Intersection of row 9 with block 7. The value <1> only appears in one or more of squares R9C1, R9C2 and R9C3 of row 9. These squares are the ones that intersect with block 7. Thus, the other (non-intersecting) squares of block 7 cannot contain this value.

R7C3 - removing <1> from <1235> leaving <235>

Intersection of column 1 with block 4. The value <7> only appears in one or more of squares R4C1, R5C1 and R6C1 of column 1. These squares are the ones that intersect with block 4. Thus, the other (non-intersecting) squares of block 4 cannot contain this value.

R5C2 - removing <7> from <157> leaving <15>

Intersection of column 3 with block 7. The values <25> only appears in one or more of squares R7C3, R8C3 and R9C3 of column 3. These squares are the ones that intersect with block 7. Thus, the other (non-intersecting) squares of block 7 cannot contain these values.

R9C2 - removing <5> from <1357> leaving <137>

Squares R2C5<123>, R2C6<23>, R3C5<136> and R3C6<36> in block 2 form a comprehensive naked quad. These 4 squares can only contain the 4 possibilities <1236>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the block.

R1C4 - removing <1> from <157> leaving <57>

R1C6 - removing <3> from <357> leaving <57>

R4C4 is the only square in column 4 that can be <1>

Intersection of block 5 with column 5. The values <79> only appears in one or more of squares R4C5, R5C5 and R6C5 of block 5. These squares are the ones that intersect with column 5. Thus, the other (non-intersecting) squares of column 5 cannot contain these values.

R8C5 - removing <7> from <237> leaving <23>

R8C2 is the only square in row 8 that can be <7>

Squares R1C4, R1C6, R9C4 and R9C6 form a Type-1 Unique Rectangle on <57>.

R9C6 - removing <57> from <2357> leaving <23>

R9C4 is the only square in row 9 that can be <7>

R1C4 can only be <5>

R1C6 can only be <7>

R9C3 is the only square in row 9 that can be <5>

R7C5 is the only square in row 7 that can be <5>

R4C9 is the only square in row 4 that can be <5>

R5C9 can only be <6>

R5C5 can only be <7>

R5C1 can only be <1>

R4C5 can only be <9>

R4C7 can only be <3>

R6C5 can only be <6>

R4C1 can only be <7>

R9C7 can only be <2>

R6C9 can only be <9>

R5C2 can only be <5>

R3C1 can only be <3>

R6C2 can only be <3>

R9C2 can only be <1>

R6C6 can only be <5>

R9C6 can only be <3>

R5C7 can only be <8>

R3C5 can only be <1>

R3C6 can only be <6>

R1C3 can only be <1>

R5C8 can only be <2>

R1C7 can only be <9>

R2C6 can only be <2>

R8C5 can only be <2>

R1C9 can only be <3>

R1C8 can only be <8>

R7C9 can only be <1>

R2C8 can only be <1>

R2C5 can only be <3>

R7C8 can only be <3>

R7C3 can only be <2>

R8C3 can only be <3>

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