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Sudoku Solution Path

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R1C3 can only be <6>
R5C7 is the only square in row 5 that can be <3>
R7C9 is the only square in row 7 that can be <9>
R8C5 is the only square in row 8 that can be <3>
R8C4 is the only square in row 8 that can be <8>
R3C5 is the only square in row 3 that can be <8>
R9C5 is the only square in row 9 that can be <5>
R1C2 is the only square in column 2 that can be <9>
R1C7 is the only square in column 7 that can be <4>
Squares R6C3 and R6C7 in row 6 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 row.
   R6C5 - removing <2> from <1249> leaving <149>
   R6C8 - removing <2> from <129> leaving <19>
Squares R2C1 and R3C1 in column 1 form a simple locked pair. These 2 squares both contain the 2 possibilities <45>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the column.
   R5C1 - removing <45> from <12456> leaving <126>
Intersection of block 5 with row 5. The value <5> only appears in one or more of squares R5C4, R5C5 and R5C6 of block 5. 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 <5> from <2578> leaving <278>
Intersection of block 8 with row 7. The values <67> only appears in one or more of squares R7C4, R7C5 and R7C6 of block 8. These squares are the ones that intersect with row 7. Thus, the other (non-intersecting) squares of row 7 cannot contain these values.
   R7C1 - removing <6> from <126> leaving <12>
Intersection of block 3 with column 9. The value <6> only appears in one or more of squares R1C9, R2C9 and R3C9 of block 3. These squares are the ones that intersect with column 9. Thus, the other (non-intersecting) squares of column 9 cannot contain this value.
   R5C9 - removing <6> from <1267> leaving <127>
   R8C9 - removing <6> from <126> leaving <12>
R8C1 is the only square in row 8 that can be <6>
Squares R4C2, R4C5 and R4C8 in row 4, R6C2, R6C5 and R6C8 in row 6 and R9C2 and R9C8 in row 9 form a Swordfish pattern on possibility <1>. All other instances of this possibility in columns 2, 5 and 8 can be removed.
   R5C2 - removing <1> from <1468> leaving <468>
   R5C5 - removing <1> from <1249> leaving <249>
   R5C8 - removing <1> from <12679> leaving <2679>
   R7C5 - removing <1> from <1267> leaving <267>
Intersection of column 5 with block 5. The value <1> only appears in one or more of squares R4C5, R5C5 and R6C5 of column 5. These squares are the ones that intersect with block 5. Thus, the other (non-intersecting) squares of block 5 cannot contain this value.
   R5C6 - removing <1> from <1259> leaving <259>
Squares R6C3, R6C7, R4C3 and R4C7 form a Type-4 Unique Rectangle on <25>.
   R4C3 - removing <2> from <257> leaving <57>
   R4C7 - removing <2> from <256> leaving <56>
Squares R1C5 and R1C8 in row 1 and R4C5 and R4C8 in row 4 form a Simple X-Wing pattern on possibility <2>. All other instances of this possibility in columns 5 and 8 can be removed.
   R2C5 - removing <2> from <2469> leaving <469>
   R5C5 - removing <2> from <249> leaving <49>
   R5C8 - removing <2> from <2679> leaving <679>
   R7C5 - removing <2> from <267> leaving <67>
   R9C8 - removing <2> from <126> leaving <16>
Squares R6C3 and R6C7 in row 6 and R9C3 and R9C7 in row 9 form a Simple X-Wing pattern on possibility <2>. All other instances of this possibility in columns 3 and 7 can be removed.
   R5C3 - removing <2> from <278> leaving <78>
Squares R2C1, R3C1, R2C4 and R3C4 form a Type-3 Unique Rectangle on <45>. Upon close inspection, it is clear that:
(R2C4 or R3C4)<26> and R7C4<26> form a locked pair on <26> in column 4. No other squares in the column can contain these possibilities
   R5C4 - removing <2> from <245> leaving <45>
Squares R7C5 (XY), R7C4 (XZ) and R1C5 (YZ) form an XY-Wing pattern on <2>. All squares that are buddies of both the XZ and YZ squares cannot be <2>.
   R2C4 - removing <2> from <2456> leaving <456>
R7C4 is the only square in column 4 that can be <2>
R7C1 can only be <1>
R8C6 can only be <1>
R8C9 can only be <2>
R7C6 can only be <7>
R2C9 can only be <6>
R9C7 can only be <6>
R9C8 can only be <1>
R4C7 can only be <5>
R9C2 can only be <8>
R6C8 can only be <9>
R3C9 can only be <7>
R3C6 can only be <5>
R5C9 can only be <1>
R1C8 can only be <2>
R4C3 can only be <7>
R6C7 can only be <2>
R5C1 can only be <2>
R6C3 can only be <5>
R7C5 can only be <6>
R9C3 can only be <2>
R1C5 can only be <7>
R3C1 can only be <4>
R2C4 can only be <4>
R4C8 can only be <6>
R5C3 can only be <8>
R4C2 can only be <1>
R5C8 can only be <7>
R5C6 can only be <9>
R5C5 can only be <4>
R2C6 can only be <2>
R2C1 can only be <5>
R2C5 can only be <9>
R3C4 can only be <6>
R5C4 can only be <5>
R4C5 can only be <2>
R6C2 can only be <4>
R5C2 can only be <6>
R6C5 can only be <1>


 

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