Nov 29 - Very Hard
Puzzle Copyright © Kevin Stone
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Reasoning
R2C9 is the only square in row 2 that can be <6>
R1C5 is the only square in row 1 that can be <6>
R3C1 is the only square in row 3 that can be <1>
R4C4 is the only square in row 4 that can be <6>
R5C6 is the only square in row 5 that can be <3>
Squares R3C4 and R3C6 in row 3 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.
R3C3 - removing <7> from <3578> leaving <358>
R3C7 - removing <7> from <3578> leaving <358>
Intersection of column 9 with block 9. The values <19> only appears in one or more of squares R7C9, R8C9 and R9C9 of column 9. These squares are the ones that intersect with block 9. Thus, the other (non-intersecting) squares of block 9 cannot contain these values.
R7C7 - removing <9> from <689> leaving <68>
Intersection of block 8 with row 7. The value <2> only appears in one or more of squares R7C4, R7C5 and R7C6 of block 8. These squares are the ones that intersect with row 7. Thus, the other (non-intersecting) squares of row 7 cannot contain this value.
R7C1 - removing <2> from <2489> leaving <489>
R7C3 - removing <2> from <268> leaving <68>
R7C9 - removing <2> from <1289> leaving <189>
Squares R7C3 and R7C7 in row 7 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.
R7C1 - removing <8> from <489> leaving <49>
R7C9 - removing <8> from <189> leaving <19>
Squares R1C2 and R9C2 in column 2 and R1C8 and R9C8 in column 8 form a Simple X-Wing pattern on possibility <8>. All other instances of this possibility in rows 1 and 9 can be removed.
R1C1 - removing <8> from <24578> leaving <2457>
R9C1 - removing <8> from <2478> leaving <247>
R1C3 - removing <8> from <23578> leaving <2357>
R9C3 - removing <8> from <2678> leaving <267>
R1C7 - removing <8> from <3578> leaving <357>
R9C7 - removing <8> from <3678> leaving <367>
R1C9 - removing <8> from <2358> leaving <235>
R9C9 - removing <8> from <1238> leaving <123>
R5C1 is the only square in column 1 that can be <8>
R5C9 can only be <5>
R4C3 can only be <5>
R5C5 can only be <1>
R6C3 can only be <7>
R5C4 can only be <7>
R9C5 can only be <4>
R6C4 can only be <2>
R6C6 can only be <8>
R6C7 can only be <9>
R4C6 can only be <4>
R6C5 can only be <5>
R4C7 can only be <8>
R4C5 can only be <9>
R7C4 can only be <1>
R7C6 can only be <2>
R3C6 can only be <7>
R7C7 can only be <6>
R3C4 can only be <4>
R7C9 can only be <9>
R7C3 can only be <8>
R7C1 can only be <4>
R8C9 can only be <2>
R8C8 can only be <7>
R1C9 can only be <3>
R1C3 can only be <2>
R3C9 can only be <8>
R9C9 can only be <1>
R3C7 can only be <5>
R1C7 can only be <7>
R3C3 can only be <3>
R9C2 can only be <7>
R8C2 can only be <5>
R9C8 can only be <8>
R9C7 can only be <3>
R9C1 can only be <2>
R2C2 can only be <4>
R1C8 can only be <4>
R9C3 can only be <6>
R2C1 can only be <7>
R1C1 can only be <5>
R2C8 can only be <2>
R8C1 can only be <9>
R1C2 can only be <8>
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