Jan 19 - Very Hard
Puzzle Copyright © Kevin Stone
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Reasoning
R6C2 can only be <7>
R6C8 can only be <3>
R4C2 can only be <5>
R6C4 can only be <9>
R6C6 can only be <4>
R5C7 can only be <2>
R5C3 can only be <6>
R5C1 can only be <4>
R6C5 can only be <6>
R1C9 is the only square in row 1 that can be <6>
R1C7 is the only square in row 1 that can be <9>
R2C6 is the only square in row 2 that can be <2>
R4C6 can only be <8>
R1C3 is the only square in row 1 that can be <2>
R1C1 is the only square in row 1 that can be <8>
R3C9 is the only square in row 3 that can be <8>
R2C4 is the only square in row 2 that can be <8>
R4C5 is the only square in row 4 that can be <2>
R7C9 is the only square in row 7 that can be <9>
R8C9 is the only square in row 8 that can be <2>
R9C1 is the only square in row 9 that can be <6>
R9C3 is the only square in row 9 that can be <8>
Squares R3C5 and R3C7 in row 3 form a simple naked pair. These 2 squares both contain the 2 possibilities <34>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the row.
R3C1 - removing <3> from <357> leaving <57>
Squares R1C5 and R3C5 in column 5 form a simple naked pair. These 2 squares both contain the 2 possibilities <34>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the column.
R5C5 - removing <3> from <1357> leaving <157>
R7C5 - removing <3> from <1357> leaving <157>
R9C5 - removing <3> from <1357> leaving <157>
Intersection of column 4 with block 5. The value <1> only appears in one or more of squares R4C4, R5C4 and R6C4 of column 4. These squares are the ones that intersect with block 5. Thus, the other (non-intersecting) squares of block 5 cannot contain this value.
R5C5 - removing <1> from <157> leaving <57>
Intersection of block 8 with row 8. The value <3> only appears in one or more of squares R8C4, R8C5 and R8C6 of block 8. These squares are the ones that intersect with row 8. Thus, the other (non-intersecting) squares of row 8 cannot contain this value.
R8C1 - removing <3> from <357> leaving <57>
Squares R3C1 and R8C1 in column 1 form a simple naked pair. These 2 squares both contain the 2 possibilities <57>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the column.
R7C1 - removing <57> from <1357> leaving <13>
Intersection of block 9 with row 9. The values <47> only appears in one or more of squares R9C7, R9C8 and R9C9 of block 9. These squares are the ones that intersect with row 9. Thus, the other (non-intersecting) squares of row 9 cannot contain these values.
R9C5 - removing <7> from <157> leaving <15>
Squares R2C9 and R9C2 form a remote naked pair. <13> can be removed from any square that is common to their groups.
R9C9 - removing <3> from <37> leaving <7>
R9C8 can only be <4>
R5C9 can only be <1>
R2C9 can only be <3>
R4C8 can only be <7>
R1C8 can only be <1>
R1C2 can only be <3>
R2C1 can only be <1>
R3C7 can only be <4>
R3C5 can only be <3>
R4C4 can only be <1>
R1C5 can only be <4>
R9C2 can only be <1>
R7C1 can only be <3>
R7C7 can only be <5>
R7C3 can only be <7>
R9C7 can only be <3>
R9C5 can only be <5>
R5C5 can only be <7>
R8C6 can only be <3>
R5C4 can only be <3>
R7C5 can only be <1>
R3C3 can only be <5>
R8C1 can only be <5>
R3C1 can only be <7>
R8C4 can only be <7>
R5C6 can only be <5>
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