Jan 13 - Super Hard
Puzzle Copyright © Kevin Stone
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Reasoning
R3C6 can only be <5>
R7C4 can only be <3>
R7C6 can only be <8>
R1C5 can only be <3>
R7C5 can only be <6>
R3C4 can only be <7>
R9C5 can only be <2>
R7C2 can only be <9>
R7C8 can only be <1>
R7C7 can only be <4>
R3C5 can only be <4>
R7C3 can only be <7>
R3C7 is the only square in row 3 that can be <1>
R3C3 is the only square in row 3 that can be <6>
R4C1 is the only square in row 4 that can be <7>
R9C1 is the only square in row 9 that can be <1>
R9C9 is the only square in row 9 that can be <7>
R6C1 is the only square in column 1 that can be <6>
Squares R4C2 and R4C8 in row 4 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.
R4C3 - removing <35> from <3459> leaving <49>
R4C5 - removing <5> from <159> leaving <19>
R4C7 - removing <35> from <3569> leaving <69>
R4C9 - removing <35> from <134569> leaving <1469>
Intersection of column 2 with block 4. The values <58> only appears in one or more of squares R4C2, R5C2 and R6C2 of column 2. These squares are the ones that intersect with block 4. Thus, the other (non-intersecting) squares of block 4 cannot contain these values.
R5C1 - removing <8> from <248> leaving <24>
R6C3 - removing <58> from <23589> leaving <239>
Intersection of column 8 with block 6. The values <58> 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.
R5C9 - removing <5> from <459> leaving <49>
R6C7 - removing <58> from <23589> leaving <239>
R6C9 - removing <5> from <1359> leaving <139>
Squares R3C2 and R3C8 in row 3 and R4C2 and R4C8 in row 4 form a Simple X-Wing pattern on possibility <3>. All other instances of this possibility in columns 2 and 8 can be removed.
R6C2 - removing <3> from <2358> leaving <258>
R6C8 - removing <3> from <2358> leaving <258>
Squares R2C1 (XY), R3C2 (XZ) and R5C1 (YZ) form an XY-Wing pattern on <2>. All squares that are buddies of both the XZ and YZ squares cannot be <2>.
R5C2 - removing <2> from <258> leaving <58>
R1C1 - removing <2> from <28> leaving <8>
R6C2 - removing <2> from <258> leaving <58>
R3C2 is the only square in column 2 that can be <2>
R3C8 can only be <3>
R1C3 can only be <5>
R4C8 can only be <5>
R4C2 can only be <3>
R1C9 can only be <6>
R1C7 can only be <2>
R4C7 is the only square in row 4 that can be <6>
Squares R9C3, R9C7, R8C3 and R8C7 form a Type-4 Unique Rectangle on <38>.
R8C3 - removing <3> from <238> leaving <28>
R8C7 - removing <3> from <358> leaving <58>
Squares R5C1 (XY), R6C3 (XZ) and R5C9 (YZ) form an XY-Wing pattern on <9>. All squares that are buddies of both the XZ and YZ squares cannot be <9>.
R6C9 - removing <9> from <139> leaving <13>
R6C7 - removing <9> from <39> leaving <3>
R6C9 can only be <1>
R9C7 can only be <8>
R9C3 can only be <3>
R8C7 can only be <5>
R8C9 can only be <3>
R2C7 can only be <9>
R8C1 can only be <2>
R2C3 can only be <4>
R2C1 can only be <3>
R4C3 can only be <9>
R2C9 can only be <5>
R4C5 can only be <1>
R4C9 can only be <4>
R6C3 can only be <2>
R5C9 can only be <9>
R5C5 can only be <5>
R6C8 can only be <8>
R8C3 can only be <8>
R5C1 can only be <4>
R6C2 can only be <5>
R5C8 can only be <2>
R5C2 can only be <8>
R6C5 can only be <9>
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