Dec 10 - Hard
Puzzle Copyright © Kevin Stone
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Reasoning
R3C2 is the only square in row 3 that can be <9>
R8C7 is the only square in row 8 that can be <9>
R8C9 is the only square in row 8 that can be <6>
R5C1 is the only square in column 1 that can be <6>
R5C2 is the only square in row 5 that can be <1>
R6C3 is the only square in column 3 that can be <2>
R3C4 is the only square in column 4 that can be <6>
Intersection of row 5 with block 6. The values <25> only appears in one or more of squares R5C7, R5C8 and R5C9 of row 5. These squares are the ones that intersect with block 6. Thus, the other (non-intersecting) squares of block 6 cannot contain these values.
R4C8 - removing <5> from <3568> leaving <368>
Intersection of row 8 with block 7. The value <7> 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 this value.
R7C1 - removing <7> from <137> leaving <13>
R7C2 - removing <7> from <3478> leaving <348>
Intersection of row 8 with block 8. The value <4> only appears in one or more of squares R8C4, R8C5 and R8C6 of row 8. 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 <348> leaving <38>
R7C6 - removing <4> from <12348> leaving <1238>
R9C5 - removing <4> from <1245> leaving <125>
Intersection of column 2 with block 4. The value <7> only appears in one or more of squares R4C2, R5C2 and R6C2 of column 2. These squares are the ones that intersect with block 4. Thus, the other (non-intersecting) squares of block 4 cannot contain this value.
R4C3 - removing <7> from <357> leaving <35>
Intersection of block 5 with row 5. The value <3> only appears in one or more of squares R5C4, R5C5 and R5C6 of block 5. These squares are the ones that intersect with row 5. Thus, the other (non-intersecting) squares of row 5 cannot contain this value.
R5C8 - removing <3> from <23458> leaving <2458>
Squares R5C4<348>, R5C5<48> and R5C6<348> in row 5 form a comprehensive naked triplet. These 3 squares can only contain the 3 possibilities <348>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the row.
R5C8 - removing <48> from <2458> leaving <25>
R5C9 - removing <4> from <245> leaving <25>
Intersection of row 5 with block 5. The values <348> 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 these values.
R4C5 - removing <8> from <678> leaving <67>
R6C5 - removing <4> from <467> leaving <67>
Squares R7C4<38>, R8C4<3458>, R8C5<458> and R8C6<348> in block 8 form a comprehensive naked quad. These 4 squares can only contain the 4 possibilities <3458>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the block.
R7C6 - removing <38> from <1238> leaving <12>
R9C5 - removing <5> from <125> leaving <12>
Intersection of row 9 with block 7. The value <5> only appears in one or more of squares R9C1, R9C2 and R9C3 of row 9. These squares are the ones that intersect with block 7. Thus, the other (non-intersecting) squares of block 7 cannot contain this value.
R8C1 - removing <5> from <357> leaving <37>
R8C3 - removing <5> from <3578> leaving <378>
Intersection of column 1 with block 1. The value <5> only appears in one or more of squares R1C1, R2C1 and R3C1 of column 1. These squares are the ones that intersect with block 1. Thus, the other (non-intersecting) squares of block 1 cannot contain this value.
R1C2 - removing <5> from <58> leaving <8>
R1C3 - removing <5> from <158> leaving <18>
R2C3 - removing <5> from <13578> leaving <1378>
R1C3 can only be <1>
R3C6 is the only square in row 3 that can be <1>
R7C6 can only be <2>
R9C5 can only be <1>
R2C7 is the only square in row 2 that can be <1>
R2C5 is the only square in row 2 that can be <2>
R3C8 is the only square in row 3 that can be <8>
R4C7 is the only square in row 4 that can be <8>
R7C1 is the only square in row 7 that can be <1>
R7C4 is the only square in row 7 that can be <8>
R2C6 is the only square in row 2 that can be <8>
R5C5 is the only square in row 5 that can be <8>
R8C3 is the only square in row 8 that can be <8>
R8C1 is the only square in row 8 that can be <7>
R3C1 can only be <5>
R3C9 can only be <7>
R2C1 can only be <3>
R7C9 can only be <4>
R7C2 can only be <3>
R2C9 can only be <5>
R9C7 can only be <3>
R9C3 can only be <5>
R9C8 can only be <2>
R7C8 can only be <7>
R5C8 can only be <5>
R2C3 can only be <7>
R2C4 can only be <4>
R5C9 can only be <2>
R6C2 can only be <7>
R9C2 can only be <4>
R4C3 can only be <3>
R5C4 can only be <3>
R1C5 can only be <5>
R4C8 can only be <6>
R4C5 can only be <7>
R1C8 can only be <4>
R6C7 can only be <4>
R5C6 can only be <4>
R8C4 can only be <5>
R8C6 can only be <3>
R6C5 can only be <6>
R4C2 can only be <5>
R6C8 can only be <3>
R1C7 can only be <6>
R8C5 can only be <4>
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