Jul 16 - Hard

Reasoning

R3C7 can only be <7>

R3C9 can only be <2>

R2C6 is the only square in row 2 that can be <2>

R5C1 is the only square in row 5 that can be <2>

R2C2 is the only square in column 2 that can be <9>

R5C2 is the only square in column 2 that can be <6>

R2C8 is the only square in column 8 that can be <6>

R2C4 can only be <4>

R2C5 can only be <3>

R3C5 can only be <8>

Squares R3C1 and R3C3 in block 1 form a simple naked pair. These 2 squares both contain the 2 possibilities <46>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the block.

R1C1 - removing <6> from <168> leaving <18>

R1C3 - removing <6> from <168> leaving <18>

Squares R1C3 and R5C3 in column 3 form a simple naked pair. These 2 squares both contain the 2 possibilities <18>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the column.

R7C3 - removing <8> from <3468> leaving <346>

R9C3 - removing <8> from <3468> leaving <346>

R7C1 is the only square in row 7 that can be <8>

R1C1 can only be <1>

R1C3 can only be <8>

R5C3 can only be <1>

R5C8 is the only square in row 5 that can be <8>

R7C3 is the only square in row 7 that can be <6>

R3C3 can only be <4>

R3C1 can only be <6>

R9C3 can only be <3>

R8C6 is the only square in column 6 that can be <3>

Intersection of column 5 with block 8. The values <14> only appears in one or more of squares R7C5, R8C5 and R9C5 of column 5. 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 <1> from <17> leaving <7>

R8C2 can only be <4>

R9C1 can only be <7>

Squares R6C2 and R6C6 in row 6 form a simple naked pair. These 2 squares both contain the 2 possibilities <78>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the row.

R6C4 - removing <8> from <189> leaving <19>

R6C9 - removing <7> from <13479> leaving <1349>

Intersection of column 7 with block 9. The value <4> only appears in one or more of squares R7C7, R8C7 and R9C7 of column 7. These squares are the ones that intersect with block 9. Thus, the other (non-intersecting) squares of block 9 cannot contain this value.

R7C9 - removing <4> from <134> leaving <13>

R9C9 - removing <4> from <459> leaving <59>

Intersection of column 8 with block 6. The value <3> only appears in one or more of squares R4C8, R5C8 and R6C8 of column 8. These squares are the ones that intersect with block 6. Thus, the other (non-intersecting) squares of block 6 cannot contain this value.

R4C9 - removing <3> from <13457> leaving <1457>

R6C9 - removing <3> from <1349> leaving <149>

Squares R7C5<14>, R8C5<15> and R9C5<45> in column 5 form a comprehensive naked triplet. These 3 squares can only contain the 3 possibilities <145>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the column.

R5C5 - removing <5> from <579> leaving <79>

R4C6 is the only square in block 5 that can be <5>

R8C8 is the only square in column 8 that can be <5>

R8C5 can only be <1>

R9C9 can only be <9>

R9C7 can only be <4>

R7C5 can only be <4>

R9C5 can only be <5>

R7C7 can only be <3>

R7C9 can only be <1>

R1C7 can only be <5>

R6C9 can only be <4>

R1C9 can only be <3>

R5C7 can only be <9>

R5C5 can only be <7>

R6C1 can only be <3>

R4C9 can only be <7>

R4C2 can only be <8>

R5C9 can only be <5>

R1C5 can only be <9>

R6C6 can only be <8>

R6C8 can only be <1>

R4C1 can only be <4>

R6C2 can only be <7>

R9C6 can only be <6>

R4C4 can only be <1>

R6C4 can only be <9>

R4C8 can only be <3>

R9C4 can only be <8>

R1C6 can only be <7>

R1C4 can only be <6>

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