Nov 07 - Very Hard
Puzzle Copyright © Kevin Stone
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Reasoning
R4C4 is the only square in row 4 that can be <6>
R5C4 is the only square in row 5 that can be <3>
R6C6 is the only square in row 6 that can be <4>
R3C6 is the only square in block 2 that can be <5>
R7C1 is the only square in column 1 that can be <5>
R9C7 is the only square in row 9 that can be <5>
Intersection of column 1 with block 1. The value <8> only appears in one or more of squares R1C1, R2C1 and R3C1 of column 1. These squares are the ones that intersect with block 1. Thus, the other (non-intersecting) squares of block 1 cannot contain this value.
R1C3 - removing <8> from <158> leaving <15>
R2C3 - removing <8> from <1478> leaving <147>
R3C3 - removing <8> from <13478> leaving <1347>
Intersection of row 1 with block 3. The value <8> only appears in one or more of squares R1C7, R1C8 and R1C9 of row 1. These squares are the ones that intersect with block 3. Thus, the other (non-intersecting) squares of block 3 cannot contain this value.
R2C7 - removing <8> from <1789> leaving <179>
R2C9 - removing <8> from <489> leaving <49>
R3C7 - removing <8> from <12678> leaving <1267>
R3C8 - removing <8> from <1278> leaving <127>
R3C9 - removing <8> from <468> leaving <46>
R7C9 is the only square in column 9 that can be <8>
R9C8 can only be <7>
R9C2 can only be <4>
R9C3 can only be <8>
Intersection of block 4 with column 3. The value <7> only appears in one or more of squares R4C3, R5C3 and R6C3 of block 4. These squares are the ones that intersect with column 3. Thus, the other (non-intersecting) squares of column 3 cannot contain this value.
R2C3 - removing <7> from <147> leaving <14>
R3C3 - removing <7> from <1347> leaving <134>
R7C3 - removing <7> from <3679> leaving <369>
R8C3 - removing <7> from <3679> leaving <369>
Squares R1C7<128>, R1C8<128> and R3C8<12> in block 3 form a comprehensive naked triplet. These 3 squares can only contain the 3 possibilities <128>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the block.
R2C7 - removing <1> from <179> leaving <79>
R3C7 - removing <12> from <1267> leaving <67>
Squares R7C2<79>, R7C4<17>, R7C6<12> and R7C8<29> in row 7 form a comprehensive naked quad. These 4 squares can only contain the 4 possibilities <1279>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the row.
R7C3 - removing <9> from <369> leaving <36>
R7C7 - removing <29> from <2369> leaving <36>
Squares R5C2 and R7C2 in column 2 and R5C8 and R7C8 in column 8 form a Simple X-Wing pattern on possibility <9>. All other instances of this possibility in rows 5 and 7 can be removed.
R5C6 - removing <9> from <19> leaving <1>
R7C6 can only be <2>
R7C8 can only be <9>
R4C6 can only be <9>
R8C5 can only be <7>
R7C2 can only be <7>
R5C8 can only be <8>
R8C9 can only be <6>
R8C1 can only be <3>
R4C5 can only be <2>
R7C4 can only be <1>
R3C9 can only be <4>
R7C7 can only be <3>
R2C9 can only be <9>
R4C3 can only be <7>
R4C7 can only be <1>
R5C5 can only be <5>
R6C7 can only be <9>
R2C7 can only be <7>
R3C2 can only be <2>
R3C4 can only be <8>
R7C3 can only be <6>
R8C7 can only be <2>
R8C3 can only be <9>
R1C7 can only be <8>
R2C1 can only be <8>
R3C7 can only be <6>
R3C8 can only be <1>
R1C2 can only be <5>
R3C1 can only be <7>
R6C4 can only be <7>
R2C5 can only be <1>
R3C3 can only be <3>
R1C8 can only be <2>
R6C3 can only be <5>
R5C2 can only be <9>
R6C5 can only be <8>
R1C3 can only be <1>
R2C3 can only be <4>
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