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Sudoku Solution Path

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Copyright © Kevin Stone

R4C2 can only be <1>
R5C5 can only be <6>
R6C2 can only be <4>
R6C8 can only be <3>
R8C4 can only be <4>
R5C8 can only be <9>
R2C5 can only be <5>
R4C5 can only be <3>
R5C2 can only be <5>
R6C5 can only be <2>
R4C8 can only be <6>
R8C6 can only be <5>
R5C4 can only be <7>
R8C1 can only be <3>
R8C5 can only be <9>
R2C6 can only be <7>
R2C4 can only be <6>
R5C6 can only be <4>
R2C7 can only be <9>
R2C1 is the only square in row 2 that can be <1>
R2C2 is the only square in row 2 that can be <3>
R8C8 is the only square in row 8 that can be <1>
R9C2 is the only square in row 9 that can be <9>
Intersection of row 9 with block 9. The value <8> only appears in one or more of squares R9C7, R9C8 and R9C9 of row 9. These squares are the ones that intersect with block 9. Thus, the other (non-intersecting) squares of block 9 cannot contain this value.
   R8C9 - removing <8> from <268> leaving <26>
Squares R7C2<27>, R8C2<278> and R8C3<78> in block 7 form a comprehensive locked triplet. These 3 squares can only contain the 3 possibilities <278>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the block.
   R7C3 - removing <7> from <457> leaving <45>
Squares R1C1 and R1C8 in row 1 and R9C1 and R9C8 in row 9 form a Simple X-Wing pattern on possibility <5>. All other instances of this possibility in columns 1 and 8 can be removed.
   R3C8 - removing <5> from <578> leaving <78>
   R7C8 - removing <5> from <2457> leaving <247>
Squares R3C2 (XYZ), R3C8 (XZ) and R1C2 (YZ) form an XYZ-Wing pattern on <7>. All squares that are buddies of all three squares cannot be <7>.
   R3C3 - removing <7> from <578> leaving <58>
R8C3 is the only square in column 3 that can be <7>
R8C7 can only be <6>
R7C2 can only be <2>
R8C9 can only be <2>
R8C2 can only be <8>
R2C8 is the only square in row 2 that can be <2>
R3C2 is the only square in row 3 that can be <6>
R1C2 can only be <7>
R1C9 is the only square in row 1 that can be <6>
Squares R1C8 and R7C3 form a remote locked pair. <45> can be removed from any square that is common to their groups.
   R7C8 - removing <4> from <47> leaving <7>
R7C7 can only be <5>
R3C8 can only be <8>
R3C3 can only be <5>
R2C9 can only be <4>
R7C3 can only be <4>
R3C7 can only be <7>
R9C8 can only be <4>
R9C1 can only be <5>
R9C9 can only be <8>
R1C8 can only be <5>
R1C1 can only be <4>
R2C3 can only be <8>

[Puzzle Code = Sudoku-20191021-SuperHard-062350]

 

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