Jan 14 - Super Hard
Puzzle Copyright © Kevin Stone
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Reasoning
R5C9 is the only square in row 5 that can be <8>
R5C8 is the only square in row 5 that can be <3>
R8C1 is the only square in row 8 that can be <8>
R9C4 is the only square in row 9 that can be <8>
R9C6 is the only square in row 9 that can be <3>
R1C4 is the only square in row 1 that can be <3>
R3C1 is the only square in row 3 that can be <3>
R7C9 is the only square in row 7 that can be <3>
R7C4 is the only square in column 4 that can be <9>
R7C6 is the only square in block 8 that can be <4>
R7C7 is the only square in row 7 that can be <6>
R9C7 is the only square in column 7 that can be <1>
Squares R8C5 and R9C5 in column 5 form a simple naked pair. These 2 squares both contain the 2 possibilities <26>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the column.
R1C5 - removing <2> from <279> leaving <79>
Intersection of row 5 with block 4. The value <5> only appears in one or more of squares R5C1, R5C2 and R5C3 of row 5. 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 <5> from <2457> leaving <247>
R4C3 - removing <5> from <4579> leaving <479>
Intersection of column 8 with block 3. The value <7> only appears in one or more of squares R1C8, R2C8 and R3C8 of column 8. These squares are the ones that intersect with block 3. Thus, the other (non-intersecting) squares of block 3 cannot contain this value.
R1C7 - removing <7> from <2789> leaving <289>
R3C7 - removing <7> from <278> leaving <28>
Squares R2C2 and R5C2 in column 2 and R2C5 and R5C5 in column 5 form a Simple X-Wing pattern on possibility <1>. All other instances of this possibility in rows 2 and 5 can be removed.
R2C1 - removing <1> from <1457> leaving <457>
R5C1 - removing <1> from <157> leaving <57>
Squares R1C2, R2C2 and R5C2 in column 2, R1C5, R2C5 and R5C5 in column 5 and R1C8 and R2C8 in column 8 form a Swordfish pattern on possibility <7>. All other instances of this possibility in rows 1, 2 and 5 can be removed.
R2C1 - removing <7> from <457> leaving <45>
R5C1 - removing <7> from <57> leaving <5>
R1C3 - removing <7> from <4578> leaving <458>
R1C6 - removing <7> from <257> leaving <25>
R2C1 can only be <4>
R1C8 is the only square in row 1 that can be <4>
R9C8 can only be <2>
R9C5 can only be <6>
R8C8 can only be <9>
R8C9 can only be <4>
R2C8 can only be <7>
R8C2 can only be <6>
R8C5 can only be <2>
R9C2 is the only square in column 2 that can be <4>
R9C3 can only be <5>
R1C3 can only be <8>
R3C7 is the only square in row 3 that can be <8>
Squares R3C3 and R7C3 in column 3 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 column.
R4C3 - removing <7> from <479> leaving <49>
R6C3 - removing <17> from <1479> leaving <49>
Squares R2C5 (XY), R3C4 (XZ) and R2C9 (YZ) form an XY-Wing pattern on <5>. All squares that are buddies of both the XZ and YZ squares cannot be <5>.
R3C9 - removing <5> from <25> leaving <2>
R1C7 can only be <9>
R1C5 can only be <7>
R2C9 can only be <5>
R2C2 can only be <1>
R1C2 can only be <5>
R5C5 can only be <1>
R3C6 can only be <5>
R2C5 can only be <9>
R5C2 can only be <7>
R3C3 can only be <7>
R7C3 can only be <1>
R3C4 can only be <1>
R1C6 can only be <2>
R4C1 can only be <2>
R6C4 can only be <4>
R6C3 can only be <9>
R4C4 can only be <5>
R7C1 can only be <7>
R4C7 can only be <7>
R6C1 can only be <1>
R4C6 can only be <6>
R6C7 can only be <2>
R6C9 can only be <6>
R4C3 can only be <4>
R6C6 can only be <7>
R4C9 can only be <9>
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