Nov 18 - Very Hard
Puzzle Copyright © Kevin Stone
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Reasoning
R4C9 is the only square in row 4 that can be <5>
R7C6 is the only square in column 6 that can be <5>
R4C6 is the only square in column 6 that can be <6>
R6C6 is the only square in column 6 that can be <7>
R5C8 is the only square in column 8 that can be <8>
R2C9 is the only square in column 9 that can be <9>
R5C9 is the only square in column 9 that can be <4>
R5C7 is the only square in row 5 that can be <3>
R8C9 is the only square in block 9 that can be <7>
Squares R2C4 and R2C8 in row 2 form a simple naked pair. These 2 squares both contain the 2 possibilities <12>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the row.
R2C1 - removing <1> from <147> leaving <47>
R2C5 - removing <12> from <1267> leaving <67>
R2C7 - removing <12> from <12467> leaving <467>
Squares R4C7 and R6C7 in column 7 form a simple naked pair. These 2 squares both contain the 2 possibilities <29>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the column.
R3C7 - removing <2> from <1267> leaving <167>
R7C7 - removing <2> from <12> leaving <1>
Squares R1C2 and R1C7 in row 1 form a simple naked pair. These 2 squares both contain the 2 possibilities <47>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the row.
R1C5 - removing <7> from <1357> leaving <135>
Squares R9C6 and R9C8 in row 9 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.
R9C2 - removing <2> from <247> leaving <47>
R9C3 - removing <3> from <1347> leaving <147>
R9C5 - removing <23> from <1234> leaving <14>
Squares R1C2 and R9C2 in column 2 form a simple naked pair. These 2 squares both contain the 2 possibilities <47>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the column.
R5C2 - removing <7> from <267> leaving <26>
R7C2 - removing <4> from <2468> leaving <268>
Squares R1C2 and R2C1 in block 1 form a simple naked pair. These 2 squares both contain the 2 possibilities <47>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the block.
R3C1 - removing <7> from <178> leaving <18>
R3C3 - removing <7> from <178> leaving <18>
Squares R3C1 and R3C3 in row 3 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 row.
R3C4 - removing <1> from <123> leaving <23>
R3C5 - removing <1> from <123567> leaving <23567>
R3C8 - removing <1> from <1235> leaving <235>
Squares R3C4 and R3C9 in row 3 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.
R3C5 - removing <23> from <23567> leaving <567>
R3C8 - removing <23> from <235> leaving <5>
R1C5 is the only square in row 1 that can be <5>
Squares R8C6 and R9C6 in block 8 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.
R7C5 - removing <23> from <2348> leaving <48>
R8C5 - removing <23> from <1238> leaving <18>
R6C5 is the only square in column 5 that can be <3>
R4C5 is the only square in column 5 that can be <2>
R4C7 can only be <9>
R6C7 can only be <2>
Intersection of column 2 with block 7. The value <8> only appears in one or more of squares R7C2, R8C2 and R9C2 of column 2. 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 <8> from <248> leaving <24>
R7C3 - removing <8> from <3468> leaving <346>
R8C1 - removing <8> from <1289> leaving <129>
R8C3 - removing <8> from <1389> leaving <139>
Squares R2C1<47>, R5C1<27> and R7C1<24> in column 1 form a comprehensive naked triplet. These 3 squares can only contain the 3 possibilities <247>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the column.
R6C1 - removing <4> from <489> leaving <89>
R8C1 - removing <2> from <129> leaving <19>
Intersection of block 4 with column 3. The value <4> only appears in one or more of squares R4C3, R5C3 and R6C3 of block 4. These squares are the ones that intersect with column 3. Thus, the other (non-intersecting) squares of column 3 cannot contain this value.
R7C3 - removing <4> from <346> leaving <36>
R9C3 - removing <4> from <147> leaving <17>
Squares R3C5, R3C7, R2C5 and R2C7 form a Type-1 Unique Rectangle on <67>.
R2C7 - removing <67> from <467> leaving <4>
R2C1 can only be <7>
R1C7 can only be <7>
R1C2 can only be <4>
R3C7 can only be <6>
R2C5 can only be <6>
R5C1 can only be <2>
R3C5 can only be <7>
R5C2 can only be <6>
R7C1 can only be <4>
R5C3 can only be <7>
R9C3 can only be <1>
R7C5 can only be <8>
R9C2 can only be <7>
R7C2 can only be <2>
R8C5 can only be <1>
R8C1 can only be <9>
R9C5 can only be <4>
R3C3 can only be <8>
R3C1 can only be <1>
R4C3 can only be <4>
R4C4 can only be <8>
R6C3 can only be <9>
R6C4 can only be <4>
R6C1 can only be <8>
R8C3 can only be <3>
R7C9 can only be <3>
R8C2 can only be <8>
R7C3 can only be <6>
R3C9 can only be <2>
R9C8 can only be <2>
R8C6 can only be <2>
R9C6 can only be <3>
R2C8 can only be <1>
R2C4 can only be <2>
R1C8 can only be <3>
R3C4 can only be <3>
R1C4 can only be <1>
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