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Sudoku Solution Path

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Sudoku Puzzle © Kevin Stone

R1C8 can only be <5>
R4C3 can only be <6>
R6C5 can only be <9>
R9C9 can only be <6>
R6C3 can only be <4>
R6C7 can only be <6>
R4C5 can only be <5>
R4C7 can only be <9>
R5C5 can only be <1>
R1C9 is the only square in row 1 that can be <4>
R2C5 is the only square in row 2 that can be <4>
R7C7 is the only square in row 7 that can be <4>
R8C4 is the only square in row 8 that can be <2>
R7C5 is the only square in column 5 that can be <7>
R2C9 is the only square in column 9 that can be <8>
Squares R7C4 and R7C8 in row 7 form a simple locked pair. These 2 squares both contain the 2 possibilities <19>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the row.
   R7C2 - removing <9> from <5689> leaving <568>
   R7C3 - removing <1> from <158> leaving <58>
   R7C6 - removing <19> from <1689> leaving <68>
Squares R8C7 and R8C9 in row 8 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 row.
   R8C3 - removing <5> from <158> leaving <18>
Squares R1C1 and R1C2 in block 1 form a simple locked pair. These 2 squares both contain the 2 possibilities <68>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the block.
   R3C2 - removing <68> from <5678> leaving <57>
   R3C3 - removing <8> from <13578> leaving <1357>
Squares R7C6 and R8C5 in block 8 form a simple locked pair. These 2 squares both contain the 2 possibilities <68>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the block.
   R8C6 - removing <68> from <1689> leaving <19>
Squares R2C6 and R8C6 in column 6 form a simple locked pair. These 2 squares both contain the 2 possibilities <19>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the column.
   R3C6 - removing <1> from <168> leaving <68>
Squares R8C7, R8C9, R5C7 and R5C9 form a Type-1 Unique Rectangle on <35>.
   R5C7 - removing <35> from <235> leaving <2>
R5C8 can only be <3>
R5C9 can only be <5>
R3C8 can only be <2>
R8C9 can only be <3>
R8C7 can only be <5>
Squares R2C7, R3C7, R2C3 and R3C3 form a Type-3 Unique Rectangle on <37>. Upon close inspection, it is clear that:
(R2C3 or R3C3)<15>, R8C3<18> and R7C3<58> form a locked triplet on <158> in column 3. No other squares in the column can contain these possibilities
   R5C3 - removing <8> from <78> leaving <7>
Intersection of column 3 with block 7. The value <8> 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.
   R7C2 - removing <8> from <568> leaving <56>
   R8C1 - removing <8> from <1689> leaving <169>
Squares R3C2 (XY), R3C4 (XZ) and R2C1 (YZ) form an XY-Wing pattern on <1>. All squares that are buddies of both the XZ and YZ squares cannot be <1>.
   R2C4 - removing <1> from <159> leaving <59>
   R2C6 - removing <1> from <19> leaving <9>
   R3C3 - removing <1> from <135> leaving <35>
R2C4 can only be <5>
R8C6 can only be <1>
R8C3 can only be <8>
R7C4 can only be <9>
R3C4 can only be <1>
R7C8 can only be <1>
R9C8 can only be <9>
R8C5 can only be <6>
R7C3 can only be <5>
R8C1 can only be <9>
R3C5 can only be <8>
R7C6 can only be <8>
R9C2 can only be <7>
R3C6 can only be <6>
R7C2 can only be <6>
R3C3 can only be <3>
R5C1 can only be <8>
R9C1 can only be <1>
R3C2 can only be <5>
R3C7 can only be <7>
R2C3 can only be <1>
R2C7 can only be <3>
R5C2 can only be <9>
R1C1 can only be <6>
R1C2 can only be <8>
R2C1 can only be <7>

 

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