Jul 02 - Hard
Puzzle Copyright © Kevin Stone
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Reasoning
R9C5 can only be <2>
R1C5 is the only square in row 1 that can be <8>
R5C5 can only be <5>
R4C5 can only be <3>
R6C5 can only be <7>
R5C4 is the only square in row 5 that can be <8>
R6C2 is the only square in row 6 that can be <8>
R6C7 is the only square in row 6 that can be <5>
R4C2 is the only square in row 4 that can be <5>
R6C8 is the only square in row 6 that can be <3>
R6C6 is the only square in row 6 that can be <9>
R7C4 is the only square in row 7 that can be <5>
R8C8 is the only square in row 8 that can be <8>
Squares R1C1 and R1C7 in row 1 form a simple naked pair. These 2 squares both contain the 2 possibilities <36>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the row.
R1C3 - removing <6> from <467> leaving <47>
R1C9 - removing <6> from <467> leaving <47>
Squares R2C4<267>, R3C4<267> and R6C4<26> in column 4 form a comprehensive naked triplet. These 3 squares can only contain the 3 possibilities <267>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the column.
R4C4 - removing <26> from <1246> leaving <14>
R8C4 - removing <7> from <147> leaving <14>
R8C6 is the only square in row 8 that can be <7>
Squares R8C2 and R8C4 in row 8 form a simple naked pair. These 2 squares both contain the 2 possibilities <14>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the row.
R8C3 - removing <14> from <1249> leaving <29>
R8C7 - removing <1> from <129> leaving <29>
R9C7 is the only square in column 7 that can be <1>
Squares R1C1<36>, R3C1<369> and R9C1<69> in column 1 form a comprehensive naked triplet. These 3 squares can only contain the 3 possibilities <369>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the column.
R5C1 - removing <6> from <126> leaving <12>
R7C1 - removing <36> from <1236> leaving <12>
R7C2 is the only square in row 7 that can be <3>
Intersection of row 7 with block 9. The value <6> only appears in one or more of squares R7C7, R7C8 and R7C9 of row 7. These squares are the ones that intersect with block 9. Thus, the other (non-intersecting) squares of block 9 cannot contain this value.
R9C9 - removing <6> from <469> leaving <49>
Intersection of column 2 with block 1. The value <6> only appears in one or more of squares R1C2, R2C2 and R3C2 of column 2. These squares are the ones that intersect with block 1. Thus, the other (non-intersecting) squares of block 1 cannot contain this value.
R1C1 - removing <6> from <36> leaving <3>
R2C3 - removing <6> from <1679> leaving <179>
R3C1 - removing <6> from <369> leaving <39>
R1C7 can only be <6>
R3C1 can only be <9>
R9C1 can only be <6>
R3C6 is the only square in row 3 that can be <3>
R2C7 is the only square in row 2 that can be <3>
R2C8 is the only square in row 2 that can be <9>
R4C7 is the only square in row 4 that can be <9>
R8C7 can only be <2>
R8C3 can only be <9>
R9C3 can only be <4>
R9C9 can only be <9>
R1C3 can only be <7>
R8C2 can only be <1>
R1C9 can only be <4>
R2C3 can only be <1>
R7C9 can only be <6>
R3C8 can only be <2>
R2C2 can only be <6>
R3C9 can only be <7>
R4C8 can only be <6>
R3C4 can only be <6>
R4C3 can only be <2>
R7C8 can only be <4>
R5C9 can only be <2>
R5C1 can only be <1>
R7C6 can only be <1>
R8C4 can only be <4>
R7C1 can only be <2>
R4C4 can only be <1>
R2C6 can only be <2>
R3C2 can only be <4>
R2C4 can only be <7>
R6C4 can only be <2>
R6C3 can only be <6>
R4C6 can only be <4>
R5C6 can only be <6>
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