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Sudoku Solution Path

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Copyright © Kevin Stone

R3C3 can only be <1>
R6C4 is the only square in row 6 that can be <3>
R6C6 is the only square in row 6 that can be <6>
R7C2 is the only square in row 7 that can be <1>
R9C8 is the only square in row 9 that can be <6>
R8C4 is the only square in row 8 that can be <6>
Squares R1C5 and R6C5 in column 5 form a simple locked pair. These 2 squares both contain the 2 possibilities <47>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the column.
   R4C5 - removing <4> from <124> leaving <12>
   R5C5 - removing <7> from <257> leaving <25>
Intersection of row 7 with block 9. The value <3> only appears in one or more of squares R7C7, R7C8 and R7C9 of row 7. These squares are the ones that intersect with block 9. Thus, the other (non-intersecting) squares of block 9 cannot contain this value.
   R8C7 - removing <3> from <238> leaving <28>
   R8C8 - removing <3> from <2348> leaving <248>
Squares R3C7 and R8C7 in column 7 form a simple locked 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.
   R2C7 - removing <28> from <2389> leaving <39>
Intersection of column 3 with block 7. The value <4> only appears in one or more of squares R7C3, R8C3 and R9C3 of column 3. These squares are the ones that intersect with block 7. Thus, the other (non-intersecting) squares of block 7 cannot contain this value.
   R8C2 - removing <4> from <23457> leaving <2357>
Squares R4C4<19>, R4C5<12> and R4C8<29> in row 4 form a comprehensive locked triplet. These 3 squares can only contain the 3 possibilities <129>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the row.
   R4C2 - removing <9> from <489> leaving <48>
   R4C6 - removing <1> from <148> leaving <48>
Squares R7C3<49>, R8C3<45>, R9C1<29> and R9C2<259> in block 7 form a comprehensive locked quad. These 4 squares can only contain the 4 possibilities <2459>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the block.
   R8C1 - removing <2> from <237> leaving <37>
   R8C2 - removing <25> from <2357> leaving <37>
Intersection of row 8 with block 9. The values <28> only appears in one or more of squares R8C7, R8C8 and R8C9 of row 8. These squares are the ones that intersect with block 9. Thus, the other (non-intersecting) squares of block 9 cannot contain these values.
   R9C9 - removing <2> from <129> leaving <19>
Squares R2C3 and R7C3 in column 3 and R2C7 and R7C7 in column 7 form a Simple X-Wing pattern on possibility <9>. All other instances of this possibility in rows 2 and 7 can be removed.
   R2C1 - removing <9> from <23789> leaving <2378>
   R2C2 - removing <9> from <235789> leaving <23578>
   R2C8 - removing <9> from <2345789> leaving <234578>
   R7C8 - removing <9> from <349> leaving <34>
   R2C9 - removing <9> from <2479> leaving <247>
Squares R8C1, R8C2, R1C1 and R1C2 form a Type-3 Unique Rectangle on <37>. Upon close inspection, it is clear that:
(R1C1 or R1C2)<59> and R2C3<59> form a locked pair on <59> in block 1. No other squares in the block can contain these possibilities
   R2C2 - removing <5> from <23578> leaving <2378>
Squares R6C5 (XY), R6C2 (XZ) and R5C4 (YZ) form an XY-Wing pattern on <9>. All squares that are buddies of both the XZ and YZ squares cannot be <9>.
   R5C1 - removing <9> from <89> leaving <8>
R5C6 can only be <5>
R4C2 can only be <4>
R5C5 can only be <2>
R8C6 can only be <1>
R2C6 can only be <4>
R9C5 can only be <5>
R4C6 can only be <8>
R1C5 can only be <7>
R6C2 can only be <9>
R4C5 can only be <1>
R6C8 can only be <7>
R9C2 can only be <2>
R6C5 can only be <4>
R5C9 can only be <9>
R9C1 can only be <9>
R2C4 can only be <1>
R4C4 can only be <9>
R4C8 can only be <2>
R5C4 can only be <7>
R3C8 can only be <8>
R1C9 can only be <4>
R9C9 can only be <1>
R1C1 can only be <3>
R7C3 can only be <4>
R1C2 can only be <5>
R8C1 can only be <7>
R2C3 can only be <9>
R1C8 can only be <9>
R8C9 can only be <2>
R2C7 can only be <3>
R7C7 can only be <9>
R3C2 can only be <7>
R3C7 can only be <2>
R2C8 can only be <5>
R8C8 can only be <4>
R7C8 can only be <3>
R8C3 can only be <5>
R8C2 can only be <3>
R2C1 can only be <2>
R8C7 can only be <8>
R2C9 can only be <7>
R2C2 can only be <8>

[Puzzle Code = Sudoku-20191019-SuperHard-327472]

 

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