Nov 30 - Hard
Puzzle Copyright © Kevin Stone
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Reasoning
R1C6 is the only square in row 1 that can be <9>
R2C5 is the only square in row 2 that can be <3>
R4C7 is the only square in row 4 that can be <7>
R6C4 is the only square in row 6 that can be <3>
R7C3 is the only square in row 7 that can be <3>
R9C9 is the only square in row 9 that can be <3>
R6C1 is the only square in column 1 that can be <9>
R5C8 is the only square in row 5 that can be <9>
R7C2 is the only square in row 7 that can be <9>
R8C7 is the only square in row 8 that can be <9>
R6C7 is the only square in column 7 that can be <8>
R6C9 is the only square in row 6 that can be <4>
R4C9 can only be <2>
R4C6 is the only square in row 4 that can be <4>
R8C9 is the only square in block 9 that can be <5>
R1C9 can only be <6>
R9C7 is the only square in column 7 that can be <6>
Squares R2C7 and R3C7 in block 3 form a simple naked pair. These 2 squares both contain the 2 possibilities <45>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the block.
R2C8 - removing <4> from <147> leaving <17>
R3C8 - removing <4> from <147> leaving <17>
Intersection of row 2 with block 1. The value <6> only appears in one or more of squares R2C1, R2C2 and R2C3 of row 2. These squares are the ones that intersect with block 1. Thus, the other (non-intersecting) squares of block 1 cannot contain this value.
R3C2 - removing <6> from <1246> leaving <124>
Intersection of row 5 with block 5. The value <5> only appears in one or more of squares R5C4, R5C5 and R5C6 of row 5. These squares are the ones that intersect with block 5. Thus, the other (non-intersecting) squares of block 5 cannot contain this value.
R4C5 - removing <5> from <158> leaving <18>
Intersection of row 7 with block 8. The values <56> only appears in one or more of squares R7C4, R7C5 and R7C6 of row 7. These squares are the ones that intersect with block 8. Thus, the other (non-intersecting) squares of block 8 cannot contain these values.
R8C4 - removing <6> from <1467> leaving <147>
R8C5 - removing <6> from <168> leaving <18>
Squares R4C5 and R8C5 in column 5 form a simple naked pair. These 2 squares both contain the 2 possibilities <18>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the column.
R3C5 - removing <1> from <1256> leaving <256>
R6C5 - removing <1> from <12> leaving <2>
R7C5 - removing <8> from <2568> leaving <256>
R6C3 can only be <1>
R5C4 can only be <5>
R5C6 can only be <8>
R5C2 can only be <2>
R4C5 can only be <1>
R4C3 can only be <5>
R4C1 can only be <8>
R1C3 can only be <7>
R8C5 can only be <8>
R8C8 can only be <4>
R9C8 can only be <2>
R7C8 can only be <8>
R1C4 can only be <1>
R8C3 can only be <6>
R1C2 can only be <8>
R8C4 can only be <7>
R1C1 can only be <5>
R8C2 can only be <1>
R2C3 can only be <2>
R9C4 can only be <4>
R9C6 can only be <1>
R9C1 can only be <7>
R2C1 can only be <1>
R2C8 can only be <7>
R3C2 can only be <4>
R2C6 can only be <5>
R3C8 can only be <1>
R3C7 can only be <5>
R2C2 can only be <6>
R3C5 can only be <6>
R2C7 can only be <4>
R7C6 can only be <2>
R3C4 can only be <2>
R7C5 can only be <5>
R7C4 can only be <6>
R3C6 can only be <7>
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