Jan 03 - Hard
Puzzle Copyright © Kevin Stone
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Reasoning
R1C1 can only be <2>
R7C2 is the only square in row 7 that can be <2>
R6C4 is the only square in column 4 that can be <3>
R3C5 is the only square in column 5 that can be <1>
R3C6 is the only square in row 3 that can be <7>
R8C4 is the only square in row 8 that can be <7>
R7C5 is the only square in column 5 that can be <4>
R2C6 is the only square in column 6 that can be <2>
R4C6 is the only square in block 5 that can be <5>
Squares R1C2 and R1C3 in row 1 form a simple naked pair. These 2 squares both contain the 2 possibilities <78>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the row.
R1C4 - removing <8> from <689> leaving <69>
R1C6 - removing <8> from <68> leaving <6>
R1C7 - removing <8> from <34689> leaving <3469>
R1C4 can only be <9>
R8C6 can only be <1>
R9C6 can only be <8>
R2C4 can only be <8>
R2C9 is the only square in row 2 that can be <9>
R2C8 is the only square in row 2 that can be <6>
R4C2 is the only square in row 4 that can be <9>
R6C7 is the only square in row 6 that can be <9>
R7C3 is the only square in row 7 that can be <8>
R1C3 can only be <7>
R1C2 can only be <8>
R3C7 is the only square in column 7 that can be <8>
Squares R2C3 and R5C3 in column 3 form a simple naked pair. These 2 squares both contain the 2 possibilities <15>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the column.
R9C3 - removing <15> from <1456> leaving <46>
R9C2 is the only square in row 9 that can be <1>
Intersection of row 9 with block 9. The values <23> 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 these values.
R8C7 - removing <3> from <3456> leaving <456>
R8C9 - removing <3> from <356> leaving <56>
Intersection of column 7 with block 9. The value <6> only appears in one or more of squares R7C7, R8C7 and R9C7 of column 7. 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 <6> from <56> leaving <5>
R9C9 - removing <6> from <2356> leaving <235>
R8C2 can only be <3>
R3C9 can only be <2>
R3C8 can only be <5>
R9C9 can only be <3>
R9C8 is the only square in row 9 that can be <2>
R9C4 is the only square in row 9 that can be <5>
R7C4 can only be <6>
R7C1 can only be <5>
R2C1 can only be <1>
R2C3 can only be <5>
R6C1 can only be <6>
R5C3 can only be <1>
R6C9 can only be <8>
R8C1 can only be <4>
R4C3 can only be <4>
R6C5 can only be <7>
R4C9 can only be <6>
R8C7 can only be <6>
R4C1 can only be <3>
R9C3 can only be <6>
R9C7 can only be <4>
R1C7 can only be <3>
R1C8 can only be <4>
R5C7 can only be <5>
R4C8 can only be <7>
R4C5 can only be <8>
R5C8 can only be <3>
R6C8 can only be <1>
R5C2 can only be <7>
R6C2 can only be <5>
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