Jun 25 - Hard
Puzzle Copyright © Kevin Stone
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Reasoning
R5C4 is the only square in row 5 that can be <1>
R4C3 is the only square in column 3 that can be <6>
R7C6 is the only square in column 6 that can be <3>
R5C9 is the only square in column 9 that can be <2>
R7C7 is the only square in column 7 that can be <2>
R9C1 is the only square in column 1 that can be <2>
R3C3 is the only square in column 3 that can be <2>
R1C9 is the only square in column 9 that can be <9>
Squares R6C7 and R6C8 in row 6 form a simple naked pair. These 2 squares both contain the 2 possibilities <69>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the row.
R6C5 - removing <69> from <5679> leaving <57>
R6C6 - removing <69> from <25679> leaving <257>
R9C6 is the only square in column 6 that can be <9>
R7C2 is the only square in column 2 that can be <9>
R4C5 is the only square in column 5 that can be <9>
Squares R2C9 and R3C9 in block 3 form a simple naked pair. These 2 squares both contain the 2 possibilities <47>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the block.
R1C8 - removing <4> from <13468> leaving <1368>
R3C8 - removing <47> from <145678> leaving <1568>
Squares R6C7 and R6C8 in block 6 form a simple naked pair. These 2 squares both contain the 2 possibilities <69>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the block.
R5C8 - removing <6> from <346> leaving <34>
Squares R4C8 and R5C8 in column 8 form a simple naked pair. These 2 squares both contain the 2 possibilities <34>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the column.
R1C8 - removing <3> from <1368> leaving <168>
Intersection of row 2 with block 1. The value <8> only appears in one or more of squares R2C1, R2C2 and R2C3 of row 2. These squares are the ones that intersect with block 1. Thus, the other (non-intersecting) squares of block 1 cannot contain this value.
R1C2 - removing <8> from <1348> leaving <134>
R3C2 - removing <8> from <148> leaving <14>
Intersection of column 3 with block 7. The values <15> 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 <15> from <1578> leaving <78>
Intersection of column 7 with block 3. The values <13> only appears in one or more of squares R1C7, R2C7 and R3C7 of column 7. These squares are the ones that intersect with block 3. Thus, the other (non-intersecting) squares of block 3 cannot contain these values.
R1C8 - removing <1> from <168> leaving <68>
R3C8 - removing <1> from <1568> leaving <568>
Intersection of block 8 with column 4. The value <4> only appears in one or more of squares R7C4, R8C4 and R9C4 of block 8. These squares are the ones that intersect with column 4. Thus, the other (non-intersecting) squares of column 4 cannot contain this value.
R1C4 - removing <4> from <2468> leaving <268>
R3C4 - removing <4> from <45678> leaving <5678>
R4C4 - removing <4> from <24> leaving <2>
R4C2 can only be <3>
R4C8 can only be <4>
R5C1 can only be <7>
R5C8 can only be <3>
R5C2 can only be <5>
R7C1 can only be <4>
R6C2 can only be <2>
R8C1 can only be <3>
R8C3 can only be <5>
R8C7 can only be <9>
R7C3 can only be <1>
R8C8 can only be <7>
R6C7 can only be <6>
R8C4 can only be <4>
R6C8 can only be <9>
R7C8 can only be <5>
R9C3 can only be <8>
R7C4 can only be <7>
R9C8 can only be <1>
R9C2 can only be <7>
R2C3 can only be <3>
R2C7 can only be <5>
R3C7 can only be <1>
R3C2 can only be <4>
R1C7 can only be <3>
R3C9 can only be <7>
R1C2 can only be <1>
R2C2 can only be <8>
R2C9 can only be <4>
R2C6 can only be <7>
R6C6 can only be <5>
R6C5 can only be <7>
R3C6 can only be <6>
R3C8 can only be <8>
R5C6 can only be <4>
R1C4 can only be <8>
R1C5 can only be <4>
R3C4 can only be <5>
R1C8 can only be <6>
R5C5 can only be <6>
R1C6 can only be <2>
R9C4 can only be <6>
R9C5 can only be <5>
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