Dec 17 - Hard
Puzzle Copyright © Kevin Stone
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Reasoning
R3C2 is the only square in row 3 that can be <5>
R4C8 is the only square in row 4 that can be <5>
R9C3 is the only square in row 9 that can be <5>
R8C6 is the only square in row 8 that can be <5>
R8C7 is the only square in column 7 that can be <8>
Squares R5C7 and R5C8 in row 5 form a simple naked pair. These 2 squares both contain the 2 possibilities <23>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the row.
R5C2 - removing <23> from <2367> leaving <67>
R5C3 - removing <23> from <2367> leaving <67>
Squares R5C2 and R5C3 in block 4 form a simple naked pair. These 2 squares both contain the 2 possibilities <67>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the block.
R4C2 - removing <7> from <127> leaving <12>
R4C3 - removing <7> from <278> leaving <28>
Squares R5C7 and R5C8 in block 6 form a simple naked pair. These 2 squares both contain the 2 possibilities <23>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the block.
R4C7 - removing <2> from <124> leaving <14>
R6C7 - removing <23> from <12349> leaving <149>
R6C8 - removing <23> from <12349> leaving <149>
Intersection of row 1 with block 1. The value <7> 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.
R2C2 - removing <7> from <23467> leaving <2346>
R2C3 - removing <7> from <23467> leaving <2346>
Intersection of row 1 with block 3. The value <1> only appears in one or more of squares R1C7, R1C8 and R1C9 of row 1. These squares are the ones that intersect with block 3. Thus, the other (non-intersecting) squares of block 3 cannot contain this value.
R2C7 - removing <1> from <123469> leaving <23469>
R2C8 - removing <1> from <123469> leaving <23469>
Intersection of row 3 with block 3. The values <24> only appears in one or more of squares R3C7, R3C8 and R3C9 of row 3. These squares are the ones that intersect with block 3. Thus, the other (non-intersecting) squares of block 3 cannot contain these values.
R2C7 - removing <24> from <23469> leaving <369>
R2C8 - removing <24> from <23469> leaving <369>
R5C7 is the only square in column 7 that can be <2>
R5C8 can only be <3>
Intersection of row 9 with block 9. The value <4> 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.
R7C8 - removing <4> from <1246> leaving <126>
R7C9 - removing <4> from <1234> leaving <123>
R8C8 - removing <4> from <146> leaving <16>
Intersection of column 1 with block 7. The value <1> only appears in one or more of squares R7C1, R8C1 and R9C1 of column 1. These squares are the ones that intersect with block 7. Thus, the other (non-intersecting) squares of block 7 cannot contain this value.
R7C2 - removing <1> from <13467> leaving <3467>
R8C2 - removing <1> from <13467> leaving <3467>
Intersection of column 5 with block 8. The value <4> only appears in one or more of squares R7C5, R8C5 and R9C5 of column 5. These squares are the ones that intersect with block 8. Thus, the other (non-intersecting) squares of block 8 cannot contain this value.
R7C4 - removing <4> from <13478> leaving <1378>
R8C4 - removing <4> from <1347> leaving <137>
Intersection of column 7 with block 3. The value <6> only appears in one or more of squares R1C7, R2C7 and R3C7 of column 7. These squares are the ones that intersect with block 3. Thus, the other (non-intersecting) squares of block 3 cannot contain this value.
R2C8 - removing <6> from <69> leaving <9>
R3C8 - removing <6> from <2469> leaving <249>
R2C5 can only be <7>
R8C5 can only be <4>
R7C5 can only be <8>
R3C5 can only be <9>
R6C7 is the only square in row 6 that can be <9>
R7C2 is the only square in row 7 that can be <4>
R2C3 is the only square in row 2 that can be <4>
R2C2 is the only square in row 2 that can be <2>
R4C2 can only be <1>
R4C7 can only be <4>
R6C2 can only be <3>
R6C8 can only be <1>
R8C8 can only be <6>
R8C2 can only be <7>
R7C8 can only be <2>
R3C8 can only be <4>
R8C3 can only be <3>
R5C2 can only be <6>
R8C4 can only be <1>
R9C1 can only be <1>
R9C7 can only be <3>
R7C1 can only be <6>
R9C9 can only be <4>
R2C7 can only be <6>
R7C9 can only be <1>
R2C4 can only be <3>
R1C7 can only be <1>
R5C3 can only be <7>
R1C3 can only be <6>
R3C1 can only be <3>
R1C9 can only be <3>
R1C1 can only be <7>
R3C9 can only be <2>
R2C6 can only be <1>
R7C4 can only be <7>
R3C6 can only be <8>
R3C4 can only be <6>
R6C6 can only be <2>
R6C3 can only be <8>
R4C6 can only be <7>
R7C6 can only be <3>
R4C4 can only be <8>
R4C3 can only be <2>
R6C4 can only be <4>
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