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Sudoku Solution Path

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Copyright © Kevin Stone

R1C9 is the only square in row 1 that can be <7>
R2C4 is the only square in row 2 that can be <6>
R7C5 is the only square in row 7 that can be <9>
R7C9 is the only square in row 7 that can be <5>
R7C3 is the only square in row 7 that can be <7>
R5C5 is the only square in row 5 that can be <7>
R9C4 is the only square in row 9 that can be <7>
R1C4 is the only square in column 4 that can be <8>
R3C3 is the only square in column 3 that can be <8>
R4C4 is the only square in column 4 that can be <5>
R5C7 is the only square in column 7 that can be <9>
R5C9 is the only square in row 5 that can be <2>
Squares R5C1 and R5C3 in block 4 form a simple locked pair. These 2 squares both contain the 2 possibilities <16>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the block.
   R4C1 - removing <1> from <1389> leaving <389>
   R4C2 - removing <1> from <137> leaving <37>
   R6C1 - removing <1> from <1389> leaving <389>
   R6C2 - removing <1> from <137> leaving <37>
Squares R4C2 and R6C2 in column 2 form a simple locked pair. These 2 squares both contain the 2 possibilities <37>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the column.
   R2C2 - removing <3> from <123> leaving <12>
   R8C2 - removing <3> from <123> leaving <12>
Squares R4C2 and R6C2 in block 4 form a simple locked pair. These 2 squares both contain the 2 possibilities <37>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the block.
   R4C1 - removing <3> from <389> leaving <89>
   R6C1 - removing <3> from <389> leaving <89>
Intersection of row 8 with block 8. The value <4> only appears in one or more of squares R8C4, R8C5 and R8C6 of row 8. These squares are the ones that intersect with block 8. Thus, the other (non-intersecting) squares of block 8 cannot contain this value.
   R9C6 - removing <4> from <1345> leaving <135>
Squares R3C1 and R3C7 in row 3 and R9C1 and R9C7 in row 9 form a Simple X-Wing pattern on possibility <2>. All other instances of this possibility in columns 1 and 7 can be removed.
   R1C1 - removing <2> from <1234> leaving <134>
   R1C7 - removing <2> from <1234> leaving <134>
R1C6 is the only square in row 1 that can be <2>
R1C5 is the only square in row 1 that can be <5>
R9C6 is the only square in row 9 that can be <5>
Squares R2C6 and R2C8 in row 2 and R8C6 and R8C8 in row 8 form a Simple X-Wing pattern on possibility <3>. All other instances of this possibility in columns 6 and 8 can be removed.
   R4C8 - removing <3> from <137> leaving <17>
   R6C8 - removing <3> from <137> leaving <17>
Squares R4C8 and R6C8 in column 8 form a simple locked pair. These 2 squares both contain the 2 possibilities <17>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the column.
   R2C8 - removing <1> from <123> leaving <23>
   R8C8 - removing <1> from <123> leaving <23>
Squares R4C8 and R6C8 in block 6 form a simple locked pair. These 2 squares both contain the 2 possibilities <17>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the block.
   R4C9 - removing <1> from <138> leaving <38>
   R6C9 - removing <1> from <138> leaving <38>
Squares R4C9 and R6C9 in column 9 form a simple locked pair. These 2 squares both contain the 2 possibilities <38>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the column.
   R3C9 - removing <3> from <134> leaving <14>
   R9C9 - removing <3> from <134> leaving <14>
Squares R3C5 and R9C5 in column 5 and R3C9 and R9C9 in column 9 form a Simple X-Wing pattern on possibility <1>. All other instances of this possibility in rows 3 and 9 can be removed.
   R3C1 - removing <1> from <1234> leaving <234>
   R9C1 - removing <1> from <1236> leaving <236>
   R9C3 - removing <1> from <136> leaving <36>
   R3C7 - removing <1> from <1234> leaving <234>
   R9C7 - removing <1> from <1234> leaving <234>
Squares R6C4, R8C4, R6C6 and R8C6 form a Type-4 Unique Rectangle on <14>.
   R6C6 - removing <1> from <149> leaving <49>
   R8C6 - removing <1> from <134> leaving <34>
Squares R2C2 (XY), R1C3 (XZ) and R2C8 (YZ) form an XY-Wing pattern on <3>. All squares that are buddies of both the XZ and YZ squares cannot be <3>.
   R1C7 - removing <3> from <134> leaving <14>
Squares R1C7 and R3C9 in block 3 form a simple locked pair. These 2 squares both contain the 2 possibilities <14>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the block.
   R3C7 - removing <4> from <234> leaving <23>
Intersection of row 1 with block 1. The value <3> 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 this value.
   R3C1 - removing <3> from <234> leaving <24>
Squares R7C1 (XY), R5C1 (XZ) and R9C3 (YZ) form an XY-Wing pattern on <6>. All squares that are buddies of both the XZ and YZ squares cannot be <6>.
   R9C1 - removing <6> from <236> leaving <23>
   R5C3 - removing <6> from <16> leaving <1>
R5C1 can only be <6>
R1C3 can only be <3>
R9C3 can only be <6>
Squares R8C2 (XY), R7C1 (XZ) and R8C8 (YZ) form an XY-Wing pattern on <3>. All squares that are buddies of both the XZ and YZ squares cannot be <3>.
   R7C7 - removing <3> from <13> leaving <1>
R7C1 can only be <3>
R1C7 can only be <4>
R9C9 can only be <4>
R3C9 can only be <1>
R1C1 can only be <1>
R3C5 can only be <3>
R9C1 can only be <2>
R9C7 can only be <3>
R3C1 can only be <4>
R8C2 can only be <1>
R9C5 can only be <1>
R3C7 can only be <2>
R8C8 can only be <2>
R2C2 can only be <2>
R2C8 can only be <3>
R2C6 can only be <1>
R8C4 can only be <4>
R8C6 can only be <3>
R6C4 can only be <1>
R4C6 can only be <9>
R4C1 can only be <8>
R6C6 can only be <4>
R6C8 can only be <7>
R6C2 can only be <3>
R4C8 can only be <1>
R4C9 can only be <3>
R6C1 can only be <9>
R4C2 can only be <7>
R6C9 can only be <8>

[Puzzle Code = Sudoku-20190712-SuperHard-038363]

 

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