Dec 14 - Very Hard
Puzzle Copyright © Kevin Stone
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Reasoning
R2C9 is the only square in row 2 that can be <6>
R2C1 is the only square in row 2 that can be <9>
R4C6 is the only square in row 4 that can be <9>
R4C1 is the only square in row 4 that can be <4>
R4C3 is the only square in row 4 that can be <8>
R5C5 is the only square in row 5 that can be <6>
R6C6 is the only square in row 6 that can be <4>
R6C7 is the only square in row 6 that can be <6>
R6C9 is the only square in row 6 that can be <3>
R6C4 is the only square in row 6 that can be <1>
R4C4 can only be <7>
R7C7 is the only square in row 7 that can be <4>
R3C5 is the only square in row 3 that can be <4>
R1C8 is the only square in row 1 that can be <4>
R1C7 is the only square in row 1 that can be <3>
R2C4 is the only square in row 2 that can be <3>
R8C8 is the only square in row 8 that can be <3>
R8C2 is the only square in row 8 that can be <4>
R8C4 is the only square in row 8 that can be <6>
R9C3 is the only square in row 9 that can be <6>
R9C5 is the only square in row 9 that can be <9>
R9C7 is the only square in column 7 that can be <8>
R1C9 is the only square in column 9 that can be <7>
R5C8 is the only square in column 8 that can be <7>
R5C2 can only be <2>
R8C1 is the only square in block 7 that can be <8>
Intersection of row 1 with block 1. The value <2> only appears in one or more of squares R1C1, R1C2 and R1C3 of row 1. These squares are the ones that intersect with block 1. Thus, the other (non-intersecting) squares of block 1 cannot contain this value.
R3C3 - removing <2> from <1257> leaving <157>
Intersection of row 9 with block 7. The value <7> only appears in one or more of squares R9C1, R9C2 and R9C3 of row 9. These squares are the ones that intersect with block 7. Thus, the other (non-intersecting) squares of block 7 cannot contain this value.
R7C3 - removing <7> from <257> leaving <25>
Squares R7C3 and R7C4 in row 7 form a simple naked 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.
R7C5 - removing <5> from <578> leaving <78>
R7C6 - removing <2> from <278> leaving <78>
Intersection of row 9 with block 9. The value <1> only appears in one or more of squares R9C7, R9C8 and R9C9 of row 9. These squares are the ones that intersect with block 9. Thus, the other (non-intersecting) squares of block 9 cannot contain this value.
R8C9 - removing <1> from <125> leaving <25>
Squares R3C3 and R3C4 in row 3 and R7C3 and R7C4 in row 7 form a Simple X-Wing pattern on possibility <5>. All other instances of this possibility in columns 3 and 4 can be removed.
R1C3 - removing <5> from <125> leaving <12>
R6C3 - removing <5> from <57> leaving <7>
R6C1 can only be <5>
R1C1 can only be <2>
R1C3 can only be <1>
R9C1 can only be <7>
R3C3 can only be <5>
R3C4 can only be <2>
R7C3 can only be <2>
R1C2 can only be <8>
R3C7 can only be <1>
R7C4 can only be <5>
R3C6 can only be <7>
R4C7 can only be <2>
R2C8 can only be <2>
R4C9 can only be <1>
R8C5 can only be <1>
R8C6 can only be <2>
R8C9 can only be <5>
R9C9 can only be <2>
R9C2 can only be <5>
R9C8 can only be <1>
R1C5 can only be <5>
R2C2 can only be <7>
R2C5 can only be <8>
R2C6 can only be <1>
R7C5 can only be <7>
R7C6 can only be <8>
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