Dec 03 - Very Hard
Puzzle Copyright © Kevin Stone
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Reasoning
R3C5 can only be <3>
R6C5 can only be <2>
R4C5 can only be <1>
R7C5 can only be <4>
R3C8 is the only square in row 3 that can be <5>
R2C2 is the only square in row 2 that can be <5>
R6C3 is the only square in row 6 that can be <9>
R6C4 is the only square in row 6 that can be <5>
R4C3 is the only square in row 4 that can be <5>
R7C3 is the only square in row 7 that can be <6>
R7C2 is the only square in row 7 that can be <7>
R9C1 can only be <3>
R9C2 can only be <9>
R8C4 is the only square in row 8 that can be <9>
R3C4 can only be <7>
R3C7 can only be <8>
R3C6 can only be <9>
R2C9 is the only square in row 2 that can be <9>
R8C3 is the only square in row 8 that can be <1>
R9C3 can only be <2>
R9C4 can only be <1>
R9C7 can only be <7>
R9C6 can only be <5>
R1C4 can only be <2>
R7C4 can only be <3>
R7C6 can only be <2>
R5C4 can only be <6>
R6C9 is the only square in column 9 that can be <8>
Intersection of row 6 with block 6. The value <3> only appears in one or more of squares R6C7, R6C8 and R6C9 of row 6. These squares are the ones that intersect with block 6. Thus, the other (non-intersecting) squares of block 6 cannot contain this value.
R4C7 - removing <3> from <2346> leaving <246>
R4C9 - removing <3> from <237> leaving <27>
R5C7 - removing <3> from <134> leaving <14>
R5C8 - removing <3> from <1347> leaving <147>
Squares R2C1 and R2C8 in row 2 and R6C1 and R6C8 in row 6 form a Simple X-Wing pattern on possibility <7>. All other instances of this possibility in columns 1 and 8 can be removed.
R1C8 - removing <7> from <1347> leaving <134>
R4C1 - removing <7> from <467> leaving <46>
R5C8 - removing <7> from <147> leaving <14>
Squares R5C7 and R5C8 in row 5 form a simple naked 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 row.
R5C2 - removing <4> from <348> leaving <38>
Squares R5C7 and R5C8 in block 6 form a simple naked 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.
R4C7 - removing <4> from <246> leaving <26>
Squares R5C7, R5C8, R1C7 and R1C8 form a Type-2 Unique Rectangle on <14>.
R1C9 - removing <3> from <37> leaving <7>
R1C3 can only be <8>
R4C9 can only be <2>
R4C7 can only be <6>
R8C9 can only be <3>
R8C8 can only be <2>
R1C6 can only be <1>
R5C3 can only be <7>
R2C1 can only be <7>
R2C6 can only be <8>
R6C1 can only be <6>
R4C1 can only be <4>
R6C7 can only be <3>
R5C6 can only be <3>
R5C2 can only be <8>
R4C6 can only be <7>
R6C8 can only be <7>
R1C7 can only be <4>
R2C8 can only be <1>
R1C8 can only be <3>
R5C7 can only be <1>
R2C7 can only be <2>
R5C8 can only be <4>
R4C2 can only be <3>
R8C1 can only be <8>
R8C2 can only be <4>
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