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Sudoku Solution Path

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R5C1 can only be <8>
R6C4 is the only square in row 6 that can be <8>
Squares R8C4 and R8C6 in row 8 form a simple locked pair. These 2 squares both contain the 2 possibilities <29>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the row.
   R8C3 - removing <9> from <159> leaving <15>
   R8C7 - removing <2> from <125> leaving <15>
Squares R4C2 and R6C2 in column 2 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 column.
   R3C2 - removing <6> from <568> leaving <58>
   R7C2 - removing <69> from <5689> leaving <58>
R7C3 is the only square in block 7 that can be <9>
Squares R4C2 and R6C2 in block 4 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 block.
   R4C3 - removing <6> from <2367> leaving <237>
   R6C3 - removing <6> from <367> leaving <37>
Squares R8C4 and R8C6 in block 8 form a simple locked pair. These 2 squares both contain the 2 possibilities <29>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the block.
   R7C4 - removing <2> from <2346> leaving <346>
   R7C5 - removing <2> from <2467> leaving <467>
   R7C6 - removing <2> from <2347> leaving <347>
Squares R4C8<49>, R5C7<349> and R5C9<34> in block 6 form a comprehensive locked triplet. These 3 squares can only contain the 3 possibilities <349>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the block.
   R4C7 - removing <349> from <34679> leaving <67>
   R6C7 - removing <39> from <13679> leaving <167>
   R6C8 - removing <9> from <19> leaving <1>
Intersection of block 6 with row 5. The value <3> only appears in one or more of squares R5C7, R5C8 and R5C9 of block 6. These squares are the ones that intersect with row 5. Thus, the other (non-intersecting) squares of row 5 cannot contain this value.
   R5C3 - removing <3> from <23> leaving <2>
Intersection of column 5 with block 2. The value <2> only appears in one or more of squares R1C5, R2C5 and R3C5 of column 5. These squares are the ones that intersect with block 2. Thus, the other (non-intersecting) squares of block 2 cannot contain this value.
   R3C4 - removing <2> from <2469> leaving <469>
   R3C6 - removing <2> from <24579> leaving <4579>
Squares R7C1<16>, R7C4<346>, R7C5<467>, R7C6<347> and R7C9<14> in row 7 form a comprehensive locked set. These 5 squares can only contain the 5 possibilities <13467>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the row.
   R7C7 - removing <14> from <12458> leaving <258>
   R7C8 - removing <4> from <24> leaving <2>
Squares R2C3 and R2C7 in row 2 and R8C3 and R8C7 in row 8 form a Simple X-Wing pattern on possibility <1>. All other instances of this possibility in columns 3 and 7 can be removed.
   R3C3 - removing <1> from <14568> leaving <4568>
   R3C7 - removing <1> from <12349> leaving <2349>
Squares R1C3 and R1C5 in row 1 and R9C3 and R9C5 in row 9 form a Simple X-Wing pattern on possibility <6>. All other instances of this possibility in columns 3 and 5 can be removed.
   R3C3 - removing <6> from <4568> leaving <458>
   R3C5 - removing <6> from <24679> leaving <2479>
   R7C5 - removing <6> from <467> leaving <47>
Squares R8C4, R8C6, R4C4 and R4C6 form a Type-4 Unique Rectangle on <29>.
   R4C4 - removing <9> from <2349> leaving <234>
   R4C6 - removing <9> from <2349> leaving <234>
Squares R9C3 (XY), R1C3 (XZ) and R9C7 (YZ) form an XY-Wing pattern on <4>. All squares that are buddies of both the XZ and YZ squares cannot be <4>.
   R1C7 - removing <4> from <24> leaving <2>
R3C5 is the only square in row 3 that can be <2>
R3C6 is the only square in row 3 that can be <7>
R7C5 is the only square in row 7 that can be <7>
R5C5 is the only square in column 5 that can be <9>
R6C6 can only be <3>
R6C3 can only be <7>
R7C6 can only be <4>
R7C9 can only be <1>
R4C6 can only be <2>
R9C5 can only be <6>
R7C1 can only be <6>
R8C7 can only be <5>
R8C3 can only be <1>
R7C7 can only be <8>
R9C3 can only be <8>
R1C5 can only be <4>
R7C4 can only be <3>
R1C3 can only be <6>
R2C4 can only be <9>
R2C6 can only be <5>
R3C4 can only be <6>
R8C4 can only be <2>
R3C1 can only be <1>
R4C4 can only be <4>
R8C6 can only be <9>
R6C7 can only be <6>
R4C3 can only be <3>
R6C2 can only be <9>
R4C7 can only be <7>
R7C2 can only be <5>
R9C7 can only be <4>
R2C3 can only be <4>
R2C7 can only be <1>
R5C7 can only be <3>
R3C3 can only be <5>
R3C2 can only be <8>
R4C8 can only be <9>
R4C2 can only be <6>
R3C8 can only be <4>
R5C9 can only be <4>
R3C7 can only be <9>
R3C9 can only be <3>


 

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