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Sudoku Solution Path

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R8C5 can only be <9>
R9C9 is the only square in column 9 that can be <5>
Squares R1C4 and R1C6 in row 1 form a simple locked pair. These 2 squares both contain the 2 possibilities <12>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the row.
   R1C1 - removing <12> from <1269> leaving <69>
   R1C3 - removing <2> from <26789> leaving <6789>
Squares R2C2 and R5C2 in column 2 form a simple locked pair. These 2 squares both contain the 2 possibilities <25>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the column.
   R3C2 - removing <25> from <1257> leaving <17>
   R7C2 - removing <2> from <1247> leaving <147>
   R8C2 - removing <5> from <145> leaving <14>
R8C3 is the only square in row 8 that can be <5>
Squares R5C8 and R8C8 in column 8 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 column.
   R2C8 - removing <6> from <268> leaving <28>
   R7C8 - removing <1> from <178> leaving <78>
Squares R1C4 and R1C6 in block 2 form a simple locked pair. These 2 squares both contain the 2 possibilities <12>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the block.
   R2C5 - removing <2> from <235> leaving <35>
   R3C5 - removing <2> from <235> leaving <35>
Squares R2C5 and R3C5 in column 5 form a simple locked 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 column.
   R4C5 - removing <35> from <3578> leaving <78>
   R5C5 - removing <35> from <2356> leaving <26>
   R6C5 - removing <3> from <2367> leaving <267>
Intersection of row 4 with block 5. The values <18> only appears in one or more of squares R4C4, R4C5 and R4C6 of row 4. These squares are the ones that intersect with block 5. Thus, the other (non-intersecting) squares of block 5 cannot contain these values.
   R5C4 - removing <1> from <12459> leaving <2459>
   R5C6 - removing <1> from <1234> leaving <234>
Intersection of row 8 with block 9. The value <6> 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 this value.
   R9C7 - removing <6> from <4678> leaving <478>
Intersection of block 8 with row 9. The value <4> only appears in one or more of squares R9C4, R9C5 and R9C6 of block 8. These squares are the ones that intersect with row 9. Thus, the other (non-intersecting) squares of row 9 cannot contain this value.
   R9C7 - removing <4> from <478> leaving <78>
Squares R7C8 and R9C7 in block 9 form a simple locked pair. These 2 squares both contain the 2 possibilities <78>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the block.
   R7C7 - removing <78> from <14789> leaving <149>
   R7C9 - removing <7> from <479> leaving <49>
Intersection of block 6 with column 9. The value <7> only appears in one or more of squares R4C9, R5C9 and R6C9 of block 6. These squares are the ones that intersect with column 9. Thus, the other (non-intersecting) squares of column 9 cannot contain this value.
   R1C9 - removing <7> from <679> leaving <69>
   R3C9 - removing <7> from <3479> leaving <349>
Squares R1C1 and R1C9 in row 1 form a simple locked pair. These 2 squares both contain the 2 possibilities <69>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the row.
   R1C3 - removing <69> from <6789> leaving <78>
   R1C7 - removing <69> from <6789> leaving <78>
Squares R1C7 and R9C7 in column 7 form a simple locked pair. These 2 squares both contain the 2 possibilities <78>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the column.
   R2C7 - removing <8> from <368> leaving <36>
   R3C7 - removing <7> from <3479> leaving <349>
Squares R6C1<239>, R6C4<29> and R6C6<23> in row 6 form a comprehensive locked triplet. These 3 squares can only contain the 3 possibilities <239>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the row.
   R6C5 - removing <2> from <267> leaving <67>
   R6C9 - removing <3> from <367> leaving <67>
Squares R1C3 and R1C7 in row 1 and R9C3 and R9C7 in row 9 form a Simple X-Wing pattern on possibility <7>. All other instances of this possibility in columns 3 and 7 can be removed.
   R3C3 - removing <7> from <279> leaving <29>
   R7C3 - removing <7> from <237> leaving <23>
Squares R3C3<29>, R5C3<239> and R7C3<23> in column 3 form a comprehensive locked triplet. These 3 squares can only contain the 3 possibilities <239>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the column.
   R2C3 - removing <2> from <268> leaving <68>
   R9C3 - removing <2> from <267> leaving <67>
Squares R1C4 and R1C6 in row 1, R6C1, R6C4 and R6C6 in row 6 and R9C1, R9C4 and R9C6 in row 9 form a Swordfish pattern on possibility <2>. All other instances of this possibility in columns 1, 4 and 6 can be removed.
   R3C1 - removing <2> from <1259> leaving <159>
   R5C4 - removing <2> from <2459> leaving <459>
   R5C6 - removing <2> from <234> leaving <34>
   R7C1 - removing <2> from <123> leaving <13>
Squares R1C1 (XY), R9C1 (XZ) and R3C3 (YZ) form an XY-Wing pattern on <2>. All squares that are buddies of both the XZ and YZ squares cannot be <2>.
   R7C3 - removing <2> from <23> leaving <3>
R7C1 can only be <1>
R8C2 can only be <4>
R7C2 can only be <7>
R7C8 can only be <8>
R3C2 can only be <1>
R9C3 can only be <6>
R7C5 can only be <2>
R2C8 can only be <2>
R9C7 can only be <7>
R9C1 can only be <2>
R2C3 can only be <8>
R1C7 can only be <8>
R1C3 can only be <7>
R2C2 can only be <5>
R3C8 can only be <7>
R5C5 can only be <6>
R9C4 can only be <4>
R9C6 can only be <8>
R2C5 can only be <3>
R5C2 can only be <2>
R3C1 can only be <9>
R2C7 can only be <6>
R3C5 can only be <5>
R8C7 can only be <1>
R1C9 can only be <9>
R3C3 can only be <2>
R1C1 can only be <6>
R6C1 can only be <3>
R5C3 can only be <9>
R5C4 can only be <5>
R4C4 can only be <1>
R5C8 can only be <1>
R6C5 can only be <7>
R5C7 can only be <3>
R8C8 can only be <6>
R6C6 can only be <2>
R4C1 can only be <5>
R6C9 can only be <6>
R4C5 can only be <8>
R6C4 can only be <9>
R1C6 can only be <1>
R1C4 can only be <2>
R4C6 can only be <3>
R7C9 can only be <4>
R4C9 can only be <7>
R5C6 can only be <4>
R3C7 can only be <4>
R7C7 can only be <9>
R3C9 can only be <3>


 

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