Jan 28 - Super Hard
Puzzle Copyright © Kevin Stone
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Reasoning
R5C5 can only be <8>
R7C4 can only be <2>
R6C9 is the only square in row 6 that can be <7>
R3C7 is the only square in column 7 that can be <5>
R6C3 is the only square in column 3 that can be <5>
Squares R3C5 and R7C5 in column 5 form a simple naked pair. These 2 squares both contain the 2 possibilities <47>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the column.
R1C5 - removing <47> from <4567> leaving <56>
R9C5 - removing <47> from <4567> leaving <56>
Intersection of row 3 with block 2. The values <48> only appears in one or more of squares R3C4, R3C5 and R3C6 of row 3. These squares are the ones that intersect with block 2. Thus, the other (non-intersecting) squares of block 2 cannot contain these values.
R1C6 - removing <4> from <2479> leaving <279>
Intersection of column 3 with block 4. The value <6> only appears in one or more of squares R4C3, R5C3 and R6C3 of column 3. These squares are the ones that intersect with block 4. Thus, the other (non-intersecting) squares of block 4 cannot contain this value.
R4C1 - removing <6> from <12468> leaving <1248>
R5C1 - removing <6> from <246> leaving <24>
Squares R5C1 and R5C7 in row 5 form a simple naked pair. These 2 squares both contain the 2 possibilities <24>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the row.
R5C9 - removing <4> from <469> leaving <69>
Squares R1C6<279>, R2C6<29>, R3C4<89>, R3C5<47> and R3C6<4789> in block 2 form a comprehensive naked set. These 5 squares can only contain the 5 possibilities <24789>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the block.
R1C4 - removing <9> from <3569> leaving <356>
R2C4 - removing <9> from <359> leaving <35>
Squares R1C1 and R1C6 in row 1 and R9C1 and R9C6 in row 9 form a Simple X-Wing pattern on possibility <7>. All other instances of this possibility in columns 1 and 6 can be removed.
R3C6 - removing <7> from <4789> leaving <489>
R7C6 - removing <7> from <147> leaving <14>
Squares R1C2 and R6C2 in column 2 and R1C8 and R6C8 in column 8 form a Simple X-Wing pattern on possibility <9>. All other instances of this possibility in rows 1 and 6 can be removed.
R1C6 - removing <9> from <279> leaving <27>
R1C9 - removing <9> from <349> leaving <34>
Squares R1C2 (XY), R1C6 (XZ) and R3C3 (YZ) form an XY-Wing pattern on <7>. All squares that are buddies of both the XZ and YZ squares cannot be <7>.
R3C5 - removing <7> from <47> leaving <4>
R1C1 - removing <7> from <257> leaving <25>
R7C5 can only be <7>
R7C3 can only be <3>
R4C3 can only be <6>
R9C2 can only be <1>
R8C1 can only be <6>
R5C3 can only be <9>
R5C9 can only be <6>
R3C3 can only be <7>
R6C2 can only be <3>
R6C7 can only be <1>
R4C2 can only be <2>
R6C1 can only be <8>
R7C7 can only be <4>
R7C6 can only be <1>
R5C7 can only be <2>
R9C8 can only be <3>
R9C1 can only be <7>
R9C9 can only be <5>
R9C5 can only be <6>
R8C9 can only be <1>
R4C7 can only be <3>
R1C2 can only be <9>
R5C1 can only be <4>
R4C9 can only be <4>
R4C8 can only be <8>
R1C9 can only be <3>
R6C8 can only be <9>
R4C1 can only be <1>
R1C8 can only be <4>
R8C6 can only be <9>
R8C4 can only be <5>
R2C6 can only be <2>
R3C6 can only be <8>
R9C4 can only be <8>
R1C5 can only be <5>
R1C1 can only be <2>
R2C4 can only be <3>
R1C4 can only be <6>
R2C9 can only be <9>
R2C1 can only be <5>
R1C6 can only be <7>
R3C4 can only be <9>
R9C6 can only be <4>
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