Sep 30 - Very Hard
Puzzle Copyright © Kevin Stone
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Reasoning
R1C3 can only be <2>
R2C3 can only be <5>
R3C3 can only be <4>
R4C3 can only be <3>
R9C3 can only be <1>
R9C7 can only be <7>
R1C2 is the only square in row 1 that can be <7>
R4C1 is the only square in row 4 that can be <7>
R7C6 is the only square in row 7 that can be <9>
R9C6 is the only square in row 9 that can be <2>
R8C8 is the only square in column 8 that can be <4>
Squares R2C1 and R2C2 in row 2 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 row.
R2C5 - removing <8> from <128> leaving <12>
R2C6 - removing <8> from <138> leaving <13>
R2C8 - removing <6> from <1236> leaving <123>
Squares R5C1 and R7C1 in column 1 form a simple naked pair. These 2 squares both contain the 2 possibilities <45>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the column.
R9C1 - removing <5> from <568> leaving <68>
Squares R7C7 and R8C7 in column 7 form a simple naked pair. These 2 squares both contain the 2 possibilities <13>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the column.
R1C7 - removing <1> from <189> leaving <89>
R6C7 - removing <3> from <389> leaving <89>
Squares R7C7 and R8C7 in block 9 form a simple naked pair. These 2 squares both contain the 2 possibilities <13>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the block.
R8C9 - removing <13> from <1356> leaving <56>
Intersection of row 4 with block 5. The value <8> only appears in one or more of squares R4C4, R4C5 and R4C6 of row 4. These squares are the ones that intersect with block 5. Thus, the other (non-intersecting) squares of block 5 cannot contain this value.
R6C4 - removing <8> from <2358> leaving <235>
R6C5 - removing <8> from <2489> leaving <249>
R6C6 - removing <8> from <358> leaving <35>
Intersection of row 5 with block 6. The value <3> 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 this value.
R6C9 - removing <3> from <358> leaving <58>
Intersection of row 9 with block 7. The value <8> 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.
R8C2 - removing <8> from <3568> leaving <356>
Intersection of column 6 with block 5. The value <5> only appears in one or more of squares R4C6, R5C6 and R6C6 of column 6. These squares are the ones that intersect with block 5. Thus, the other (non-intersecting) squares of block 5 cannot contain this value.
R4C4 - removing <5> from <158> leaving <18>
R6C4 - removing <5> from <235> leaving <23>
Squares R4C4<18>, R7C4<15> and R8C4<158> in column 4 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 column.
R1C4 - removing <18> from <168> leaving <6>
R3C4 - removing <8> from <2368> leaving <236>
R3C6 is the only square in block 2 that can be <8>
Intersection of row 1 with block 3. The values <189> 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 these values.
R2C8 - removing <1> from <123> leaving <23>
Squares R2C1, R2C2, R9C1 and R9C2 form a Type-1 Unique Rectangle on <68>.
R9C2 - removing <68> from <568> leaving <5>
R9C8 can only be <6>
R7C1 can only be <4>
R9C1 can only be <8>
R8C9 can only be <5>
R7C2 can only be <3>
R5C1 can only be <5>
R7C7 can only be <1>
R8C2 can only be <6>
R7C4 can only be <5>
R8C7 can only be <3>
R2C2 can only be <8>
R6C9 can only be <8>
R2C1 can only be <6>
R6C7 can only be <9>
R1C9 can only be <1>
R1C8 can only be <9>
R5C9 can only be <3>
R3C9 can only be <6>
R6C2 can only be <4>
R1C7 can only be <8>
R5C8 can only be <1>
R4C8 can only be <5>
R6C5 can only be <2>
R5C2 can only be <9>
R6C4 can only be <3>
R2C5 can only be <1>
R2C6 can only be <3>
R8C5 can only be <8>
R2C8 can only be <2>
R6C6 can only be <5>
R3C4 can only be <2>
R3C8 can only be <3>
R4C6 can only be <1>
R5C5 can only be <4>
R8C4 can only be <1>
R4C5 can only be <9>
R4C4 can only be <8>
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