Oct 01 - Hard
Puzzle Copyright © Kevin Stone
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Reasoning
R8C8 can only be <5>
R1C1 is the only square in row 1 that can be <9>
R2C8 is the only square in row 2 that can be <4>
R3C7 is the only square in row 3 that can be <2>
R4C1 is the only square in row 4 that can be <2>
R8C1 can only be <4>
R7C5 is the only square in row 7 that can be <2>
R8C5 is the only square in row 8 that can be <9>
R2C1 is the only square in column 1 that can be <6>
Squares R7C7 and R9C8 in block 9 form a simple naked pair. These 2 squares both contain the 2 possibilities <68>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the block.
R9C9 - removing <8> from <278> leaving <27>
Intersection of row 3 with block 2. The values <15> only appears in one or more of squares R3C4, R3C5 and R3C6 of row 3. These squares are the ones that intersect with block 2. Thus, the other (non-intersecting) squares of block 2 cannot contain these values.
R1C4 - removing <15> from <145678> leaving <4678>
R1C5 - removing <5> from <5678> leaving <678>
R1C6 - removing <15> from <14567> leaving <467>
R2C5 - removing <5> from <358> leaving <38>
Intersection of column 1 with block 4. The value <5> only appears in one or more of squares R4C1, R5C1 and R6C1 of column 1. These squares are the ones that intersect with block 4. Thus, the other (non-intersecting) squares of block 4 cannot contain this value.
R5C2 - removing <5> from <578> leaving <78>
Intersection of column 7 with block 6. The values <45> only appears in one or more of squares R4C7, R5C7 and R6C7 of column 7. These squares are the ones that intersect with block 6. Thus, the other (non-intersecting) squares of block 6 cannot contain these values.
R4C9 - removing <5> from <3589> leaving <389>
R5C9 - removing <5> from <1589> leaving <189>
R6C9 - removing <5> from <3589> leaving <389>
Squares R7C4<567>, R7C6<567> and R9C5<67> in block 8 form a comprehensive naked triplet. These 3 squares can only contain the 3 possibilities <567>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the block.
R9C4 - removing <67> from <1467> leaving <14>
R9C6 - removing <67> from <1467> leaving <14>
Squares R1C2<58>, R1C8<18> and R1C9<158> in row 1 form a comprehensive naked triplet. These 3 squares can only contain the 3 possibilities <158>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the row.
R1C4 - removing <8> from <4678> leaving <467>
R1C5 - removing <8> from <678> leaving <67>
Squares R1C5 and R9C5 in column 5 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 column.
R5C5 - removing <67> from <5678> leaving <58>
Squares R5C1 and R5C5 in row 5 form a simple naked pair. These 2 squares both contain the 2 possibilities <58>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the row.
R5C2 - removing <8> from <78> leaving <7>
R5C3 - removing <8> from <4789> leaving <479>
R5C7 - removing <58> from <4568> leaving <46>
R5C8 - removing <8> from <168> leaving <16>
R5C9 - removing <8> from <189> leaving <19>
R8C2 can only be <2>
R8C9 can only be <7>
R9C9 can only be <2>
R9C5 is the only square in row 9 that can be <7>
R1C5 can only be <6>
R7C3 is the only square in row 7 that can be <7>
R7C7 is the only square in row 7 that can be <8>
R9C8 can only be <6>
R5C8 can only be <1>
R5C9 can only be <9>
R1C8 can only be <8>
R5C3 can only be <4>
R1C2 can only be <5>
R2C9 can only be <5>
R1C9 can only be <1>
R5C7 can only be <6>
R6C7 can only be <5>
R4C7 can only be <4>
R5C1 is the only square in column 1 that can be <5>
R5C5 can only be <8>
R2C5 can only be <3>
R4C4 can only be <5>
R2C2 can only be <8>
R3C5 can only be <5>
R3C6 can only be <1>
R3C4 can only be <8>
R9C6 can only be <4>
R4C6 can only be <9>
R7C4 can only be <6>
R7C6 can only be <5>
R6C4 can only be <7>
R9C4 can only be <1>
R1C6 can only be <7>
R1C4 can only be <4>
R6C6 can only be <6>
R9C2 can only be <3>
R3C3 can only be <3>
R4C3 can only be <8>
R4C9 can only be <3>
R6C3 can only be <9>
R6C1 can only be <3>
R6C9 can only be <8>
R9C1 can only be <8>
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