Dec 31 - Hard
Puzzle Copyright © Kevin Stone
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Reasoning
R4C1 can only be <3>
R2C4 is the only square in row 2 that can be <3>
R4C2 is the only square in row 4 that can be <4>
R5C8 is the only square in row 5 that can be <3>
R6C5 is the only square in row 6 that can be <8>
Squares R3C2 and R3C3 in row 3 form a simple naked pair. These 2 squares both contain the 2 possibilities <59>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the row.
R3C6 - removing <59> from <1259> leaving <12>
R3C8 - removing <59> from <1579> leaving <17>
R3C9 - removing <5> from <257> leaving <27>
Squares R3C2 and R3C3 in block 1 form a simple naked pair. These 2 squares both contain the 2 possibilities <59>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the block.
R1C2 - removing <59> from <3589> leaving <38>
R1C3 - removing <59> from <3569> leaving <36>
R2C1 - removing <59> from <5689> leaving <68>
Intersection of row 8 with block 7. The values <39> only appears in one or more of squares R8C1, R8C2 and R8C3 of row 8. These squares are the ones that intersect with block 7. Thus, the other (non-intersecting) squares of block 7 cannot contain these values.
R7C1 - removing <9> from <5679> leaving <567>
R7C2 - removing <9> from <259> leaving <25>
Intersection of column 4 with block 5. The values <49> 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 these values.
R5C6 - removing <9> from <1269> leaving <126>
Intersection of block 8 with row 8. The values <57> 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 these values.
R8C1 - removing <57> from <5679> leaving <69>
R8C2 - removing <5> from <12359> leaving <1239>
R8C3 - removing <5> from <13569> leaving <1369>
R8C9 - removing <57> from <2567> leaving <26>
R3C9 is the only square in column 9 that can be <7>
R3C8 can only be <1>
R3C6 can only be <2>
R4C7 is the only square in column 7 that can be <1>
R4C5 can only be <7>
R4C6 can only be <6>
R5C6 can only be <1>
R5C5 can only be <2>
R2C5 is the only square in row 2 that can be <1>
R8C5 can only be <5>
R8C6 can only be <7>
R5C9 is the only square in row 5 that can be <6>
R8C9 can only be <2>
R1C7 is the only square in row 1 that can be <2>
R5C4 is the only square in row 5 that can be <4>
R6C4 can only be <9>
R6C3 is the only square in row 6 that can be <1>
Squares R9C3 and R9C7 in row 9 form a simple naked pair. These 2 squares both contain the 2 possibilities <56>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the row.
R9C1 - removing <56> from <5678> leaving <78>
R9C2 - removing <5> from <1258> leaving <128>
R9C4 - removing <6> from <126> leaving <12>
R9C8 - removing <56> from <567> leaving <7>
R9C1 can only be <8>
R2C1 can only be <6>
R8C1 can only be <9>
R1C3 can only be <3>
R5C1 can only be <5>
R1C2 can only be <8>
R8C3 can only be <6>
R5C2 can only be <9>
R7C1 can only be <7>
R3C2 can only be <5>
R8C4 can only be <1>
R9C3 can only be <5>
R8C2 can only be <3>
R9C4 can only be <2>
R9C7 can only be <6>
R3C3 can only be <9>
R7C2 can only be <2>
R9C2 can only be <1>
R7C4 can only be <6>
R1C9 can only be <5>
R1C6 can only be <9>
R6C9 can only be <4>
R2C7 can only be <9>
R2C6 can only be <5>
R2C8 can only be <4>
R7C7 can only be <5>
R1C8 can only be <6>
R2C9 can only be <8>
R6C8 can only be <5>
R7C8 can only be <9>
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