Dec 08 - Super Hard
Puzzle Copyright © Kevin Stone
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Reasoning
R6C1 can only be <8>
R5C4 is the only square in row 5 that can be <1>
R6C5 is the only square in row 6 that can be <4>
R7C5 is the only square in row 7 that can be <7>
R5C6 is the only square in row 5 that can be <7>
R4C1 is the only square in row 4 that can be <7>
Squares R5C2 and R5C3 in row 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 row.
R5C5 - removing <2> from <2359> leaving <359>
R5C8 - removing <6> from <3569> leaving <359>
Intersection of column 8 with block 9. The value <6> only appears in one or more of squares R7C8, R8C8 and R9C8 of column 8. These squares are the ones that intersect with block 9. Thus, the other (non-intersecting) squares of block 9 cannot contain this value.
R7C9 - removing <6> from <1469> leaving <149>
R9C9 - removing <6> from <4569> leaving <459>
Intersection of block 8 with row 9. The value <6> only appears in one or more of squares R9C4, R9C5 and R9C6 of block 8. These squares are the ones that intersect with row 9. Thus, the other (non-intersecting) squares of row 9 cannot contain this value.
R9C3 - removing <6> from <2346> leaving <234>
Squares R1C3 and R1C9 in row 1 and R9C3 and R9C9 in row 9 form a Simple X-Wing pattern on possibility <4>. All other instances of this possibility in columns 3 and 9 can be removed.
R2C3 - removing <4> from <345> leaving <35>
R7C9 - removing <4> from <149> leaving <19>
Squares R7C1 and R7C9 in row 7 form a simple naked pair. These 2 squares both contain the 2 possibilities <19>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the row.
R7C2 - removing <1> from <146> leaving <46>
R7C8 - removing <9> from <469> leaving <46>
Squares R2C3, R2C5 and R2C8 in row 2, R5C5 and R5C8 in row 5 and R8C3 and R8C5 in row 8 form a Swordfish pattern on possibility <3>. All other instances of this possibility in columns 3, 5 and 8 can be removed.
R1C3 - removing <3> from <2345> leaving <245>
R3C5 - removing <3> from <2358> leaving <258>
R3C8 - removing <3> from <35> leaving <5>
R4C5 - removing <3> from <238> leaving <28>
R9C3 - removing <3> from <234> leaving <24>
Squares R3C5 and R4C5 in column 5 form a simple naked pair. These 2 squares both contain the 2 possibilities <28>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the column.
R2C5 - removing <8> from <358> leaving <35>
Squares R2C3 and R2C5 in row 2 form a simple naked pair. These 2 squares both contain the 2 possibilities <35>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the row.
R2C8 - removing <3> from <349> leaving <49>
R5C8 is the only square in column 8 that can be <3>
R4C9 can only be <6>
Squares R1C4 and R4C4 in column 4 form a simple naked pair. These 2 squares both contain the 2 possibilities <23>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the column.
R9C4 - removing <3> from <369> leaving <69>
Squares R2C7 and R2C8 in row 2, R5C5 and R5C7 in row 5 and R8C5, R8C7 and R8C8 in row 8 form a Swordfish pattern on possibility <9>. All other instances of this possibility in columns 5, 7 and 8 can be removed.
R9C7 - removing <9> from <259> leaving <25>
Squares R7C2 (XY), R9C3 (XZ) and R5C2 (YZ) form an XY-Wing pattern on <2>. All squares that are buddies of both the XZ and YZ squares cannot be <2>.
R5C3 - removing <2> from <26> leaving <6>
R8C2 - removing <2> from <126> leaving <16>
R5C2 can only be <2>
Squares R8C2 (XY), R7C1 (XZ) and R8C8 (YZ) form an XY-Wing pattern on <9>. All squares that are buddies of both the XZ and YZ squares cannot be <9>.
R7C9 - removing <9> from <19> leaving <1>
R7C1 can only be <9>
R3C9 can only be <3>
R1C9 can only be <4>
R2C8 can only be <9>
R2C7 can only be <8>
R8C8 can only be <6>
R8C2 can only be <1>
R7C8 can only be <4>
R2C2 can only be <4>
R1C7 can only be <1>
R7C2 can only be <6>
R3C2 can only be <8>
R3C5 can only be <2>
R3C1 can only be <1>
R4C5 can only be <8>
R1C4 can only be <3>
R4C6 can only be <3>
R4C4 can only be <2>
R9C6 can only be <6>
R9C4 can only be <9>
R6C6 can only be <5>
R1C1 can only be <2>
R2C5 can only be <5>
R2C3 can only be <3>
R5C5 can only be <9>
R1C6 can only be <8>
R5C7 can only be <5>
R8C5 can only be <3>
R6C4 can only be <6>
R9C7 can only be <2>
R6C9 can only be <9>
R9C9 can only be <5>
R8C3 can only be <2>
R9C1 can only be <3>
R9C3 can only be <4>
R8C7 can only be <9>
R1C3 can only be <5>
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