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Jun 24 - Very Hard

## Reasoning

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

R5C8 is the only square in row 5 that can be <3>

R5C2 is the only square in row 5 that can be <9>

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

R7C1 is the only square in row 7 that can be <3>

R7C7 is the only square in row 7 that can be <9>

R2C9 is the only square in row 2 that can be <9>

R8C6 is the only square in row 8 that can be <2>

R8C9 is the only square in row 8 that can be <6>

R8C3 is the only square in row 8 that can be <9>

R5C1 is the only square in column 1 that can be <2>

Squares R4C3 and R9C3 in column 3 form a simple naked pair. These 2 squares both contain the 2 possibilities <17>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the column.

R1C3 - removing <1> from <123> leaving <23>

R2C3 - removing <1> from <136> leaving <36>

R3C3 - removing <1> from <1236> leaving <236>

Squares R8C7 and R9C7 in column 7 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 column.

R1C7 - removing <8> from <2348> leaving <234>

R2C7 - removing <8> from <348> leaving <34>

R6C7 - removing <8> from <248> leaving <24>

Squares R8C7 and R9C7 in block 9 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 block.

R8C8 - removing <8> from <178> leaving <17>

R9C8 - removing <8> from <178> leaving <17>

Squares R9C3 and R9C8 in row 9 form a simple naked pair. These 2 squares both contain the 2 possibilities <17>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the row.

R9C1 - removing <1> from <145> leaving <45>

R9C5 - removing <7> from <4578> leaving <458>

Squares R8C8 and R9C8 in column 8 form a simple naked pair. These 2 squares both contain the 2 possibilities <17>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the column.

R2C8 - removing <1> from <148> leaving <48>

R4C8 - removing <7> from <478> leaving <48>

Intersection of row 7 with block 8. The values <157> only appears in one or more of squares R7C4, R7C5 and R7C6 of row 7. These squares are the ones that intersect with block 8. Thus, the other (non-intersecting) squares of block 8 cannot contain these values.

R8C4 - removing <157> from <14578> leaving <48>

R9C5 - removing <5> from <458> leaving <48>

Squares R1C5 and R9C5 in column 5 form a simple naked pair. These 2 squares both contain the 2 possibilities <48>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the column.

R3C5 - removing <8> from <68> leaving <6>

R5C5 - removing <8> from <5678> leaving <567>

R2C3 is the only square in row 2 that can be <6>

R5C6 is the only square in row 5 that can be <6>

Squares R2C6 and R4C6 in column 6 and R2C8 and R4C8 in column 8 form a Simple X-Wing pattern on possibility <4>. All other instances of this possibility in rows 2 and 4 can be removed.

R2C4 - removing <4> from <13478> leaving <1378>

R2C7 - removing <4> from <34> leaving <3>

R1C3 is the only square in row 1 that can be <3>

R3C3 can only be <2>

R3C4 is the only square in row 3 that can be <3>

Squares R2C1 and R4C1 in column 1 and R2C8 and R4C8 in column 8 form a Simple X-Wing pattern on possibility <8>. All other instances of this possibility in rows 2 and 4 can be removed.

R2C2 - removing <8> from <158> leaving <15>

R2C4 - removing <8> from <178> leaving <17>

R2C6 - removing <8> from <1478> leaving <147>

R4C6 - removing <8> from <478> leaving <47>

R3C6 is the only square in column 6 that can be <8>

R3C9 can only be <1>

R1C5 can only be <4>

R1C7 can only be <2>

R9C5 can only be <8>

R1C9 can only be <8>

R6C7 can only be <4>

R1C2 can only be <1>

R5C9 can only be <7>

R2C8 can only be <4>

R4C8 can only be <8>

R4C1 can only be <1>

R5C5 can only be <5>

R6C9 can only be <2>

R9C7 can only be <5>

R8C4 can only be <4>

R9C1 can only be <4>

R8C7 can only be <8>

R2C2 can only be <5>

R2C1 can only be <8>

R8C2 can only be <7>

R4C3 can only be <7>

R4C6 can only be <4>

R9C3 can only be <1>

R6C2 can only be <8>

R5C4 can only be <8>

R7C5 can only be <7>

R6C4 can only be <7>

R2C4 can only be <1>

R7C6 can only be <1>

R7C4 can only be <5>

R2C6 can only be <7>

R8C8 can only be <1>

R8C1 can only be <5>

R9C8 can only be <7>

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