Jul 24 - Very Hard
Puzzle Copyright © Kevin Stone
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Reasoning
R7C5 can only be <8>
R9C4 can only be <4>
R5C8 is the only square in column 8 that can be <4>
R8C2 is the only square in column 2 that can be <4>
Intersection of column 8 with block 3. The value <8> only appears in one or more of squares R1C8, R2C8 and R3C8 of column 8. These squares are the ones that intersect with block 3. Thus, the other (non-intersecting) squares of block 3 cannot contain this value.
R1C9 - removing <8> from <1238> leaving <123>
R2C9 - removing <8> from <1389> leaving <139>
Intersection of block 2 with row 1. The value <5> only appears in one or more of squares R1C4, R1C5 and R1C6 of block 2. These squares are the ones that intersect with row 1. Thus, the other (non-intersecting) squares of row 1 cannot contain this value.
R1C1 - removing <5> from <1358> leaving <138>
R1C2 - removing <5> from <13578> leaving <1378>
R1C8 - removing <5> from <12358> leaving <1238>
Squares R5C2<138>, R5C3<18> and R5C4<138> in row 5 form a comprehensive naked triplet. These 3 squares can only contain the 3 possibilities <138>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the row.
R5C5 - removing <13> from <1236> leaving <26>
Squares R5C5 and R8C5 in column 5 form a simple naked pair. These 2 squares both contain the 2 possibilities <26>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the column.
R6C5 - removing <2> from <2347> leaving <347>
Squares R5C5 and R8C5 in column 5 and R5C7 and R8C7 in column 7 form a Simple X-Wing pattern on possibility <2>. All other instances of this possibility in rows 5 and 8 can be removed.
R5C6 - removing <2> from <269> leaving <69>
R8C8 - removing <2> from <235> leaving <35>
R8C9 - removing <2> from <237> leaving <37>
Squares R3C8<135>, R7C8<15> and R8C8<35> in column 8 form a comprehensive naked triplet. These 3 squares can only contain the 3 possibilities <135>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the column.
R1C8 - removing <13> from <1238> leaving <28>
R2C8 - removing <135> from <13589> leaving <89>
R9C8 - removing <1> from <129> leaving <29>
Squares R3C2 and R3C8 in row 3 and R7C2 and R7C8 in row 7 form a Simple X-Wing pattern on possibility <5>. All other instances of this possibility in columns 2 and 8 can be removed.
R2C2 - removing <5> from <135678> leaving <13678>
R8C8 - removing <5> from <35> leaving <3>
R8C9 can only be <7>
R8C3 can only be <8>
R5C3 can only be <1>
R2C3 can only be <7>
R1C6 is the only square in row 1 that can be <7>
R6C6 can only be <2>
R6C9 can only be <8>
R9C6 can only be <6>
R5C5 can only be <6>
R6C4 can only be <3>
R4C9 can only be <9>
R9C1 can only be <1>
R5C6 can only be <9>
R8C5 can only be <2>
R4C6 can only be <5>
R5C7 can only be <2>
R8C7 can only be <5>
R6C1 can only be <4>
R5C4 can only be <8>
R8C1 can only be <6>
R2C7 can only be <9>
R7C8 can only be <1>
R9C2 can only be <7>
R9C9 can only be <2>
R7C2 can only be <5>
R9C8 can only be <9>
R2C8 can only be <8>
R1C8 can only be <2>
R5C2 can only be <3>
R4C4 can only be <1>
R6C5 can only be <7>
R4C1 can only be <8>
R3C8 can only be <5>
R1C1 can only be <3>
R4C5 can only be <4>
R1C4 can only be <5>
R3C2 can only be <1>
R1C9 can only be <1>
R2C1 can only be <5>
R1C2 can only be <8>
R2C9 can only be <3>
R2C5 can only be <1>
R3C5 can only be <3>
R2C2 can only be <6>
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