Oct 03 - Very Hard
Puzzle Copyright © Kevin Stone
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Reasoning
R1C9 can only be <8>
R3C4 can only be <1>
R7C4 can only be <8>
R8C4 can only be <6>
R6C5 is the only square in row 6 that can be <6>
Squares R6C3 and R6C7 in row 6 form a simple naked pair. These 2 squares both contain the 2 possibilities <38>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the row.
R6C2 - removing <38> from <3489> leaving <49>
R6C8 - removing <38> from <3489> leaving <49>
Intersection of block 5 with row 5. The values <19> only appears in one or more of squares R5C4, R5C5 and R5C6 of block 5. These squares are the ones that intersect with row 5. Thus, the other (non-intersecting) squares of row 5 cannot contain these values.
R5C1 - removing <9> from <34789> leaving <3478>
R5C2 - removing <9> from <234789> leaving <23478>
R5C8 - removing <9> from <23489> leaving <2348>
R5C9 - removing <9> from <249> leaving <24>
Intersection of column 1 with block 7. The value <9> only appears in one or more of squares R7C1, R8C1 and R9C1 of column 1. 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 <9> from <123489> leaving <12348>
R9C2 - removing <9> from <289> leaving <28>
Intersection of column 9 with block 9. The value <9> 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 this value.
R8C8 - removing <9> from <45789> leaving <4578>
R9C8 - removing <9> from <5689> leaving <568>
Squares R6C2 and R6C8 in row 6 and R7C2 and R7C8 in row 7 form a Simple X-Wing pattern on possibility <4>. All other instances of this possibility in columns 2 and 8 can be removed.
R4C2 - removing <4> from <2349> leaving <239>
R4C8 - removing <4> from <23459> leaving <2359>
R5C2 - removing <4> from <23478> leaving <2378>
R5C8 - removing <4> from <2348> leaving <238>
R8C2 - removing <4> from <12348> leaving <1238>
R8C8 - removing <4> from <4578> leaving <578>
R4C5 is the only square in row 4 that can be <4>
R5C4 can only be <9>
R2C4 can only be <4>
R2C6 is the only square in row 2 that can be <9>
R8C6 is the only square in column 6 that can be <5>
R9C5 can only be <2>
R9C2 can only be <8>
R9C1 can only be <9>
R9C9 can only be <6>
R9C8 can only be <5>
R2C9 can only be <2>
R5C9 can only be <4>
R8C9 can only be <9>
R6C8 can only be <9>
R6C2 can only be <4>
R7C2 can only be <1>
R7C6 can only be <7>
R7C8 can only be <4>
R3C6 can only be <3>
R8C5 can only be <1>
R5C5 can only be <3>
R5C6 can only be <1>
R1C8 is the only square in row 1 that can be <1>
R2C3 is the only square in row 2 that can be <1>
R2C1 is the only square in row 2 that can be <8>
R5C1 can only be <7>
R5C2 can only be <2>
R1C1 can only be <3>
R5C8 can only be <8>
R8C2 can only be <3>
R4C3 can only be <3>
R8C8 can only be <7>
R6C7 can only be <3>
R6C3 can only be <8>
R2C7 can only be <7>
R4C7 can only be <5>
R4C8 can only be <2>
R8C1 can only be <4>
R8C3 can only be <2>
R4C2 can only be <9>
R8C7 can only be <8>
R3C8 can only be <6>
R2C5 can only be <5>
R3C2 can only be <7>
R2C8 can only be <3>
R2C2 can only be <6>
R1C5 can only be <7>
R1C2 can only be <5>
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