Mar 11 - Very Hard
Puzzle Copyright © Kevin Stone
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Reasoning
R2C7 is the only square in row 2 that can be <7>
R3C2 is the only square in row 3 that can be <7>
R4C9 is the only square in row 4 that can be <7>
R5C1 is the only square in row 5 that can be <7>
R9C5 is the only square in row 9 that can be <7>
R2C8 is the only square in column 8 that can be <4>
R5C9 is the only square in column 9 that can be <5>
Squares R1C9 and R3C9 in block 3 form a simple naked pair. These 2 squares both contain the 2 possibilities <28>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the block.
R1C7 - removing <28> from <1268> leaving <16>
R3C8 - removing <28> from <1268> leaving <16>
Intersection of column 1 with block 7. The value <1> 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.
R7C2 - removing <1> from <1349> leaving <349>
R9C3 - removing <1> from <1356> leaving <356>
Intersection of column 5 with block 5. The value <8> only appears in one or more of squares R4C5, R5C5 and R6C5 of column 5. 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 <23568> leaving <2356>
Squares R9C1<15>, R9C7<158> and R9C8<18> in row 9 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 row.
R9C3 - removing <5> from <356> leaving <36>
R9C4 - removing <8> from <368> leaving <36>
R7C4 is the only square in column 4 that can be <8>
R5C4 is the only square in column 4 that can be <4>
Squares R2C4 and R9C4 in column 4 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.
R3C4 - removing <6> from <256> leaving <25>
R6C4 - removing <36> from <2356> leaving <25>
Squares R7C1<19>, R7C7<129> and R7C8<129> in row 7 form a comprehensive naked triplet. These 3 squares can only contain the 3 possibilities <129>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the row.
R7C2 - removing <9> from <349> leaving <34>
R7C6 - removing <2> from <234> leaving <34>
Intersection of row 7 with block 9. The value <2> 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 this value.
R8C7 - removing <2> from <259> leaving <59>
Squares R6C1 and R7C1 in column 1 and R6C8 and R7C8 in column 8 form a Simple X-Wing pattern on possibility <9>. All other instances of this possibility in rows 6 and 7 can be removed.
R6C2 - removing <9> from <39> leaving <3>
R6C7 - removing <9> from <2689> leaving <268>
R7C7 - removing <9> from <129> leaving <12>
R4C2 can only be <1>
R7C2 can only be <4>
R7C6 can only be <3>
R9C4 can only be <6>
R9C3 can only be <3>
R2C4 can only be <3>
R4C5 is the only square in row 4 that can be <3>
R4C8 is the only square in row 4 that can be <8>
R9C8 can only be <1>
R9C1 can only be <5>
R3C8 can only be <6>
R7C7 can only be <2>
R1C7 can only be <1>
R7C8 can only be <9>
R6C7 can only be <6>
R7C1 can only be <1>
R6C8 can only be <2>
R8C7 can only be <5>
R9C7 can only be <8>
R6C1 can only be <9>
R5C3 can only be <2>
R5C7 can only be <9>
R6C4 can only be <5>
R6C5 can only be <8>
R4C3 can only be <5>
R3C4 can only be <2>
R4C6 can only be <2>
R3C9 can only be <8>
R3C3 can only be <1>
R1C9 can only be <2>
R8C6 can only be <4>
R8C5 can only be <2>
R1C6 can only be <6>
R1C2 can only be <9>
R1C5 can only be <4>
R5C6 can only be <1>
R2C5 can only be <1>
R2C3 can only be <6>
R5C5 can only be <6>
R3C6 can only be <5>
R1C3 can only be <8>
R8C2 can only be <6>
R8C3 can only be <9>
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