Feb 01 - Super Hard
Puzzle Copyright © Kevin Stone
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Reasoning
R3C6 can only be <3>
R7C4 can only be <9>
R1C8 is the only square in row 1 that can be <3>
R6C8 can only be <7>
R2C8 can only be <9>
R4C8 can only be <8>
R9C8 can only be <5>
R8C8 can only be <2>
R3C7 is the only square in row 3 that can be <2>
R1C2 is the only square in row 1 that can be <2>
R3C5 is the only square in row 3 that can be <9>
R1C1 is the only square in row 1 that can be <9>
R5C9 is the only square in row 5 that can be <2>
R7C6 is the only square in row 7 that can be <2>
R7C7 is the only square in row 7 that can be <8>
R9C2 is the only square in row 9 that can be <8>
Squares R6C2 and R6C7 in row 6 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 row.
R6C3 - removing <4> from <456> leaving <56>
R6C5 - removing <3> from <356> leaving <56>
Squares R2C1 and R9C1 in column 1 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 column.
R5C1 - removing <14> from <1345> leaving <35>
R8C1 - removing <14> from <1345> leaving <35>
Squares R1C5 and R3C4 in block 2 form a simple naked pair. These 2 squares both contain the 2 possibilities <17>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the block.
R2C4 - removing <17> from <1678> leaving <68>
Intersection of block 5 with column 5. The values <36> only appears in one or more of squares R4C5, R5C5 and R6C5 of block 5. These squares are the ones that intersect with column 5. Thus, the other (non-intersecting) squares of column 5 cannot contain these values.
R9C5 - removing <6> from <146> leaving <14>
R9C9 is the only square in row 9 that can be <6>
R8C9 can only be <4>
Squares R5C1<35>, R5C4<78>, R5C5<357> and R5C6<58> in row 5 form a comprehensive naked quad. These 4 squares can only contain the 4 possibilities <3578>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the row.
R5C3 - removing <57> from <1457> leaving <14>
R5C7 - removing <3> from <134> leaving <14>
Intersection of row 5 with block 5. The values <78> only appears in one or more of squares R5C4, R5C5 and R5C6 of row 5. These squares are the ones that intersect with block 5. Thus, the other (non-intersecting) squares of block 5 cannot contain these values.
R4C5 - removing <7> from <367> leaving <36>
Squares R6C3 and R6C5 in row 6 and R7C3 and R7C5 in row 7 form a Simple X-Wing pattern on possibility <5>. All other instances of this possibility in columns 3 and 5 can be removed.
R5C5 - removing <5> from <357> leaving <37>
Squares R2C1 and R9C1 in column 1, R1C5 and R9C5 in column 5 and R1C9 and R2C9 in column 9 form a Swordfish pattern on possibility <1>. All other instances of this possibility in rows 1, 2 and 9 can be removed.
R2C2 - removing <1> from <147> leaving <47>
Squares R3C3 (XY), R5C3 (XZ) and R2C2 (YZ) form an XY-Wing pattern on <4>. All squares that are buddies of both the XZ and YZ squares cannot be <4>.
R6C2 - removing <4> from <34> leaving <3>
R6C7 can only be <4>
R8C2 can only be <1>
R5C1 can only be <5>
R5C7 can only be <1>
R8C4 can only be <6>
R4C2 can only be <7>
R9C1 can only be <4>
R8C6 can only be <5>
R2C4 can only be <8>
R8C1 can only be <3>
R5C6 can only be <8>
R7C5 can only be <4>
R9C5 can only be <1>
R2C1 can only be <1>
R7C3 can only be <5>
R1C5 can only be <7>
R1C9 can only be <1>
R5C5 can only be <3>
R3C4 can only be <1>
R2C9 can only be <7>
R3C3 can only be <7>
R2C6 can only be <6>
R5C4 can only be <7>
R2C2 can only be <4>
R6C3 can only be <6>
R4C5 can only be <6>
R5C3 can only be <4>
R4C7 can only be <3>
R6C5 can only be <5>
R4C3 can only be <1>
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