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Sudoku Solution Path

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Copyright © Kevin Stone

R4C9 can only be <2>
R6C4 can only be <9>
R5C7 can only be <6>
R5C8 can only be <3>
R6C9 can only be <7>
R6C6 can only be <8>
R4C4 can only be <4>
R6C1 can only be <6>
R5C5 can only be <2>
R4C6 can only be <1>
R1C4 can only be <7>
R4C1 can only be <9>
R9C4 can only be <2>
R1C9 is the only square in row 1 that can be <3>
R1C8 is the only square in row 1 that can be <6>
R8C8 can only be <9>
R8C5 can only be <7>
R7C7 can only be <1>
R9C7 can only be <7>
R8C9 can only be <6>
R2C1 is the only square in row 2 that can be <7>
R9C1 is the only square in row 9 that can be <3>
R9C3 is the only square in row 9 that can be <6>
R9C9 is the only square in row 9 that can be <5>
R2C9 is the only square in column 9 that can be <1>
Intersection of row 1 with block 1. The values <18> only appears in one or more of squares R1C1, R1C2 and R1C3 of row 1. These squares are the ones that intersect with block 1. Thus, the other (non-intersecting) squares of block 1 cannot contain these values.
   R2C2 - removing <8> from <489> leaving <49>
   R3C1 - removing <8> from <258> leaving <25>
   R3C3 - removing <8> from <589> leaving <59>
Squares R3C1<25>, R3C3<59> and R3C7<29> in row 3 form a comprehensive locked triplet. These 3 squares can only contain the 3 possibilities <259>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the row.
   R3C5 - removing <9> from <489> leaving <48>
Squares R3C5 and R3C9 in row 3 and R7C5 and R7C9 in row 7 form a Simple X-Wing pattern on possibility <4>. All other instances of this possibility in columns 5 and 9 can be removed.
   R2C5 - removing <4> from <489> leaving <89>
Squares R5C2, R5C3, R1C2 and R1C3 form a Type-3 Unique Rectangle on <18>. Upon close inspection, it is clear that:
(R1C2 or R1C3)<249>, R3C3<59>, R3C1<25> and R2C2<49> form a locked quad on <2459> in block 1. No other squares in the block can contain these possibilities
   R1C1 - removing <2> from <128> leaving <18>
Squares R2C2 (XY), R2C8 (XZ) and R9C2 (YZ) form an XY-Wing pattern on <8>. All squares that are buddies of both the XZ and YZ squares cannot be <8>.
   R9C8 - removing <8> from <48> leaving <4>
R9C6 can only be <9>
R2C8 can only be <8>
R7C9 can only be <8>
R2C5 can only be <9>
R3C9 can only be <4>
R3C5 can only be <8>
R7C1 can only be <5>
R9C2 can only be <8>
R1C6 can only be <4>
R7C5 can only be <4>
R2C2 can only be <4>
R7C3 can only be <9>
R3C1 can only be <2>
R3C3 can only be <5>
R5C2 can only be <1>
R3C7 can only be <9>
R8C1 can only be <1>
R1C7 can only be <2>
R5C3 can only be <8>
R1C2 can only be <9>
R8C2 can only be <2>
R1C3 can only be <1>
R1C1 can only be <8>

[Puzzle Code = Sudoku-20190416-SuperHard-071585]

 

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