Feb 05 - Very Hard
Puzzle Copyright © Kevin Stone
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Reasoning
R2C5 is the only square in row 2 that can be <1>
R2C9 is the only square in row 2 that can be <4>
R4C1 is the only square in row 4 that can be <8>
R3C3 is the only square in row 3 that can be <8>
R1C7 is the only square in row 1 that can be <8>
R1C9 is the only square in row 1 that can be <2>
R5C3 is the only square in row 5 that can be <4>
R6C4 is the only square in row 6 that can be <8>
R7C1 is the only square in row 7 that can be <5>
R2C3 is the only square in row 2 that can be <5>
R7C5 is the only square in row 7 that can be <8>
R8C1 is the only square in row 8 that can be <4>
R3C1 is the only square in column 1 that can be <2>
R1C3 is the only square in column 3 that can be <9>
R1C5 is the only square in column 5 that can be <5>
R1C4 can only be <6>
R1C6 can only be <3>
R3C5 can only be <7>
R5C4 is the only square in column 4 that can be <5>
R9C3 is the only square in block 7 that can be <1>
Squares R3C4 and R3C6 in row 3 form a simple naked pair. These 2 squares both contain the 2 possibilities <49>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the row.
R3C9 - removing <9> from <369> leaving <36>
Squares R6C1 and R6C3 in row 6 form a simple naked pair. These 2 squares both contain the 2 possibilities <37>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the row.
R6C2 - removing <3> from <135> leaving <15>
R6C8 - removing <3> from <356> leaving <56>
R6C9 - removing <37> from <1367> leaving <16>
Squares R3C2 and R8C2 in column 2 form a simple naked pair. These 2 squares both contain the 2 possibilities <36>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the column.
R5C2 - removing <3> from <123> leaving <12>
Squares R4C6 and R5C6 in column 6 form a simple naked pair. These 2 squares both contain the 2 possibilities <17>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the column.
R7C6 - removing <7> from <467> leaving <46>
R9C6 - removing <7> from <679> leaving <69>
Intersection of row 7 with block 9. The values <13> only appears in one or more of squares R7C7, R7C8 and R7C9 of row 7. These squares are the ones that intersect with block 9. Thus, the other (non-intersecting) squares of block 9 cannot contain these values.
R8C7 - removing <3> from <23679> leaving <2679>
R8C9 - removing <3> from <3679> leaving <679>
R9C7 - removing <3> from <23679> leaving <2679>
Intersection of row 8 with block 9. The value <9> only appears in one or more of squares R8C7, R8C8 and R8C9 of row 8. These squares are the ones that intersect with block 9. Thus, the other (non-intersecting) squares of block 9 cannot contain this value.
R9C7 - removing <9> from <2679> leaving <267>
Intersection of column 8 with block 6. The values <25> only appears in one or more of squares R4C8, R5C8 and R6C8 of column 8. These squares are the ones that intersect with block 6. Thus, the other (non-intersecting) squares of block 6 cannot contain these values.
R4C7 - removing <2> from <1279> leaving <179>
R5C7 - removing <2> from <1237> leaving <137>
Squares R4C6<17>, R4C7<179> and R4C9<179> in row 4 form a comprehensive naked triplet. These 3 squares can only contain the 3 possibilities <179>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the row.
R4C2 - removing <1> from <125> leaving <25>
R4C8 - removing <9> from <259> leaving <25>
R2C8 is the only square in column 8 that can be <9>
Squares R2C7 and R8C2 form a remote naked pair. <36> can be removed from any square that is common to their groups.
R8C7 - removing <6> from <2679> leaving <279>
Squares R3C2 and R3C9 in row 3 and R8C2 and R8C9 in row 8 form a Simple X-Wing pattern on possibility <6>. All other instances of this possibility in columns 2 and 9 can be removed.
R6C9 - removing <6> from <16> leaving <1>
R7C9 - removing <6> from <1367> leaving <137>
R6C2 can only be <5>
R6C8 can only be <6>
R4C2 can only be <2>
R7C8 can only be <3>
R7C9 can only be <7>
R5C8 can only be <2>
R7C4 can only be <4>
R4C9 can only be <9>
R4C8 can only be <5>
R5C2 can only be <1>
R4C7 can only be <7>
R8C9 can only be <6>
R5C6 can only be <7>
R5C7 can only be <3>
R4C6 can only be <1>
R2C7 can only be <6>
R7C6 can only be <6>
R3C4 can only be <9>
R7C7 can only be <1>
R9C6 can only be <9>
R8C2 can only be <3>
R3C9 can only be <3>
R9C7 can only be <2>
R9C4 can only be <7>
R3C6 can only be <4>
R9C5 can only be <3>
R8C7 can only be <9>
R2C1 can only be <3>
R3C2 can only be <6>
R8C3 can only be <7>
R8C5 can only be <2>
R6C3 can only be <3>
R9C1 can only be <6>
R6C1 can only be <7>
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