Aug 20 - Hard
Puzzle Copyright © Kevin Stone
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Reasoning
R2C5 is the only square in row 2 that can be <6>
R8C6 is the only square in row 8 that can be <6>
R9C3 is the only square in row 9 that can be <3>
R9C7 is the only square in row 9 that can be <6>
R4C7 is the only square in column 7 that can be <1>
R4C4 is the only square in row 4 that can be <3>
R1C8 is the only square in column 8 that can be <6>
R1C9 is the only square in row 1 that can be <7>
R2C9 is the only square in column 9 that can be <2>
R5C9 is the only square in column 9 that can be <3>
R5C8 is the only square in row 5 that can be <8>
R7C6 is the only square in row 7 that can be <8>
Squares R6C6 and R9C6 in column 6 form a simple naked pair. These 2 squares both contain the 2 possibilities <59>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the column.
R1C6 - removing <59> from <2359> leaving <23>
R3C6 - removing <9> from <239> leaving <23>
Squares R1C7 and R3C7 in column 7 form a simple naked pair. These 2 squares both contain the 2 possibilities <39>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the column.
R5C7 - removing <9> from <459> leaving <45>
R7C7 - removing <9> from <459> leaving <45>
Squares R1C6 and R3C6 in block 2 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.
R1C5 - removing <2> from <12459> leaving <1459>
Intersection of row 9 with block 8. The value <5> only appears in one or more of squares R9C4, R9C5 and R9C6 of row 9. These squares are the ones that intersect with block 8. Thus, the other (non-intersecting) squares of block 8 cannot contain this value.
R7C4 - removing <5> from <4579> leaving <479>
Intersection of column 4 with block 8. The value <7> only appears in one or more of squares R7C4, R8C4 and R9C4 of column 4. These squares are the ones that intersect with block 8. Thus, the other (non-intersecting) squares of block 8 cannot contain this value.
R9C5 - removing <7> from <14579> leaving <1459>
Squares R6C5<579>, R6C6<59> and R6C8<579> in row 6 form a comprehensive naked triplet. These 3 squares can only contain the 3 possibilities <579>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the row.
R6C2 - removing <79> from <14679> leaving <146>
R6C3 - removing <7> from <1467> leaving <146>
R6C9 - removing <9> from <49> leaving <4>
R8C9 can only be <8>
R5C7 can only be <5>
R9C9 can only be <9>
R9C6 can only be <5>
R7C8 can only be <5>
R7C7 can only be <4>
R7C3 can only be <7>
R6C6 can only be <9>
R6C8 can only be <7>
R6C5 can only be <5>
R4C8 can only be <9>
R7C4 can only be <9>
R2C4 can only be <1>
R3C4 can only be <4>
R2C1 can only be <9>
R1C4 can only be <5>
R9C4 can only be <7>
R4C2 can only be <7>
R1C5 can only be <9>
R1C7 can only be <3>
R1C6 can only be <2>
R3C7 can only be <9>
R3C2 can only be <6>
R3C3 can only be <2>
R6C2 can only be <1>
R3C6 can only be <3>
R5C3 can only be <4>
R4C5 can only be <2>
R4C1 can only be <5>
R5C5 can only be <7>
R5C1 can only be <2>
R5C2 can only be <9>
R1C3 can only be <1>
R6C3 can only be <6>
R9C2 can only be <4>
R9C5 can only be <1>
R8C1 can only be <1>
R9C1 can only be <8>
R8C5 can only be <4>
R1C1 can only be <4>
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