Feb 03 - Super Hard
Puzzle Copyright © Kevin Stone
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Reasoning
R1C4 can only be <6>
R7C9 can only be <8>
R8C4 can only be <1>
R9C4 can only be <4>
R2C4 can only be <9>
R5C4 can only be <8>
R4C2 is the only square in row 4 that can be <4>
R2C3 is the only square in row 2 that can be <4>
R7C1 is the only square in row 7 that can be <1>
R7C8 is the only square in row 7 that can be <4>
R1C3 is the only square in column 3 that can be <5>
R8C3 is the only square in column 3 that can be <8>
R8C5 is the only square in column 5 that can be <2>
R8C6 is the only square in row 8 that can be <5>
R3C9 is the only square in column 9 that can be <1>
R6C9 is the only square in column 9 that can be <5>
Squares R4C5 and R4C9 in row 4 form a simple naked pair. These 2 squares both contain the 2 possibilities <79>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the row.
R4C1 - removing <7> from <378> leaving <38>
R4C8 - removing <7> from <378> leaving <38>
Squares R9C3 and R9C6 in row 9 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.
R9C1 - removing <36> from <3679> leaving <79>
R9C7 - removing <3> from <2379> leaving <279>
Squares R1C1 and R4C1 in column 1 form a simple naked pair. These 2 squares both contain the 2 possibilities <38>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the column.
R3C1 - removing <3> from <369> leaving <69>
R6C1 - removing <8> from <678> leaving <67>
Squares R6C1 and R6C5 in row 6 form a simple naked pair. These 2 squares both contain the 2 possibilities <67>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the row.
R6C2 - removing <67> from <2678> leaving <28>
R6C8 - removing <7> from <278> leaving <28>
Squares R7C2 and R9C3 in block 7 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 block.
R8C2 - removing <3> from <379> leaving <79>
Intersection of column 7 with block 3. The value <8> 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 this value.
R2C8 - removing <8> from <5678> leaving <567>
Intersection of column 8 with block 6. The values <28> 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 these values.
R5C7 - removing <2> from <2379> leaving <379>
Squares R1C7<278>, R1C9<27> and R2C7<78> in block 3 form a comprehensive naked triplet. These 3 squares can only contain the 3 possibilities <278>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the block.
R2C8 - removing <7> from <567> leaving <56>
Squares R3C2 and R3C5 in row 3 and R7C2 and R7C5 in row 7 form a Simple X-Wing pattern on possibility <3>. All other instances of this possibility in columns 2 and 5 can be removed.
R5C2 - removing <3> from <2367> leaving <267>
Squares R5C3 and R9C3 in column 3 and R5C6 and R9C6 in column 6 form a Simple X-Wing pattern on possibility <6>. All other instances of this possibility in rows 5 and 9 can be removed.
R5C2 - removing <6> from <267> leaving <27>
R5C5 - removing <6> from <1679> leaving <179>
Squares R5C2 and R8C2 in column 2 and R5C8 and R8C8 in column 8 form a Simple X-Wing pattern on possibility <7>. All other instances of this possibility in rows 5 and 8 can be removed.
R5C5 - removing <7> from <179> leaving <19>
R5C6 - removing <7> from <167> leaving <16>
R5C7 - removing <7> from <379> leaving <39>
R8C7 - removing <7> from <379> leaving <39>
Squares R5C7 and R8C7 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.
R9C7 - removing <9> from <279> leaving <27>
Intersection of column 6 with block 2. The value <7> only appears in one or more of squares R1C6, R2C6 and R3C6 of column 6. These squares are the ones that intersect with block 2. Thus, the other (non-intersecting) squares of block 2 cannot contain this value.
R2C5 - removing <7> from <157> leaving <15>
Squares R5C3<36>, R5C5<19>, R5C6<16> and R5C7<39> in row 5 form a comprehensive naked quad. These 4 squares can only contain the 4 possibilities <1369>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the row.
R5C8 - removing <3> from <237> leaving <27>
Squares R2C2 (XY), R7C2 (XZ) and R1C1 (YZ) form an XY-Wing pattern on <3>. All squares that are buddies of both the XZ and YZ squares cannot be <3>.
R3C2 - removing <3> from <369> leaving <69>
R3C5 is the only square in row 3 that can be <3>
R7C5 can only be <6>
R1C6 can only be <7>
R7C2 can only be <3>
R6C5 can only be <7>
R9C6 can only be <3>
R9C3 can only be <6>
R1C9 can only be <2>
R2C6 can only be <1>
R1C7 can only be <8>
R2C5 can only be <5>
R5C6 can only be <6>
R5C3 can only be <3>
R6C1 can only be <6>
R4C5 can only be <9>
R1C1 can only be <3>
R2C7 can only be <7>
R2C8 can only be <6>
R9C7 can only be <2>
R2C2 can only be <8>
R3C8 can only be <5>
R4C9 can only be <7>
R5C5 can only be <1>
R9C9 can only be <9>
R5C8 can only be <2>
R5C7 can only be <9>
R4C1 can only be <8>
R8C7 can only be <3>
R5C2 can only be <7>
R6C8 can only be <8>
R3C1 can only be <9>
R6C2 can only be <2>
R4C8 can only be <3>
R8C8 can only be <7>
R8C2 can only be <9>
R9C1 can only be <7>
R3C2 can only be <6>
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