Dec 30 - Hard
Puzzle Copyright © Kevin Stone
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Reasoning
R6C5 can only be <6>
R4C8 is the only square in row 4 that can be <6>
R3C9 is the only square in row 3 that can be <6>
R7C1 is the only square in row 7 that can be <6>
R9C2 is the only square in column 2 that can be <7>
R9C8 is the only square in column 8 that can be <4>
R5C8 is the only square in column 8 that can be <7>
R5C5 can only be <4>
R4C7 can only be <5>
R4C5 can only be <7>
R4C2 is the only square in column 2 that can be <4>
R4C3 can only be <9>
R7C2 is the only square in row 7 that can be <9>
R3C1 is the only square in row 3 that can be <9>
Intersection of row 3 with block 1. The value <2> only appears in one or more of squares R3C1, R3C2 and R3C3 of row 3. These squares are the ones that intersect with block 1. Thus, the other (non-intersecting) squares of block 1 cannot contain this value.
R1C1 - removing <2> from <1258> leaving <158>
R1C2 - removing <2> from <1258> leaving <158>
Intersection of row 7 with block 9. The value <3> only appears in one or more of squares R7C7, R7C8 and R7C9 of row 7. These squares are the ones that intersect with block 9. Thus, the other (non-intersecting) squares of block 9 cannot contain this value.
R9C9 - removing <3> from <235> leaving <25>
Squares R7C7<123>, R7C8<135>, R7C9<235> and R9C9<25> in block 9 form a comprehensive naked quad. These 4 squares can only contain the 4 possibilities <1235>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the block.
R8C7 - removing <12> from <1278> leaving <78>
R8C9 - removing <25> from <2578> leaving <78>
Intersection of block 9 with row 7. The values <13> only appears in one or more of squares R7C7, R7C8 and R7C9 of block 9. These squares are the ones that intersect with row 7. Thus, the other (non-intersecting) squares of row 7 cannot contain these values.
R7C3 - removing <1> from <125> leaving <25>
Squares R6C3 and R7C3 in column 3 form a simple naked pair. These 2 squares both contain the 2 possibilities <25>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the column.
R2C3 - removing <5> from <1345> leaving <134>
R3C3 - removing <25> from <235> leaving <3>
R8C3 - removing <25> from <1245> leaving <14>
R3C7 can only be <8>
R3C8 can only be <5>
R8C7 can only be <7>
R3C2 can only be <2>
R8C9 can only be <8>
R5C9 can only be <2>
R9C9 can only be <5>
R6C7 can only be <3>
R6C8 can only be <8>
R2C7 can only be <1>
R6C2 can only be <5>
R7C9 can only be <3>
R2C3 can only be <4>
R7C7 can only be <2>
R1C8 can only be <3>
R6C3 can only be <2>
R7C3 can only be <5>
R7C8 can only be <1>
R1C9 can only be <9>
R2C9 can only be <7>
R8C3 can only be <1>
R8C4 can only be <6>
R9C1 can only be <2>
R1C4 can only be <8>
R9C6 can only be <9>
R8C1 can only be <4>
R9C5 can only be <3>
R2C6 can only be <5>
R1C2 can only be <1>
R2C4 can only be <3>
R9C4 can only be <1>
R2C1 can only be <8>
R2C5 can only be <9>
R8C6 can only be <2>
R1C5 can only be <2>
R8C5 can only be <5>
R1C6 can only be <6>
R1C1 can only be <5>
R5C2 can only be <8>
R5C1 can only be <1>
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