Sep 03 - Very Hard
Puzzle Copyright © Kevin Stone
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Reasoning
R1C7 can only be <6>
R5C6 can only be <7>
R9C4 can only be <1>
R5C5 can only be <1>
R5C4 can only be <8>
R7C4 can only be <9>
R5C2 can only be <3>
R5C8 can only be <5>
R4C5 can only be <9>
R7C6 can only be <5>
R3C4 can only be <6>
R4C2 can only be <1>
R6C5 can only be <2>
R9C2 can only be <5>
R3C5 can only be <5>
R2C5 can only be <4>
R4C1 can only be <8>
R4C9 can only be <6>
R6C1 can only be <9>
R1C2 is the only square in row 1 that can be <4>
R2C1 is the only square in row 2 that can be <5>
R7C9 is the only square in row 7 that can be <4>
R8C7 is the only square in row 8 that can be <5>
Intersection of row 2 with block 3. The values <28> only appears in one or more of squares R2C7, R2C8 and R2C9 of row 2. These squares are the ones that intersect with block 3. Thus, the other (non-intersecting) squares of block 3 cannot contain these values.
R1C8 - removing <2> from <239> leaving <39>
R3C9 - removing <2> from <1237> leaving <137>
Squares R7C1<137>, R8C1<137> and R9C3<37> in block 7 form a comprehensive naked triplet. These 3 squares can only contain the 3 possibilities <137>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the block.
R7C3 - removing <37> from <378> leaving <8>
R8C3 - removing <37> from <36789> leaving <689>
R2C7 is the only square in column 7 that can be <8>
Squares R1C8<39>, R2C8<29> and R9C8<23> in column 8 form a comprehensive naked triplet. These 3 squares can only contain the 3 possibilities <239>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the column.
R8C8 - removing <3> from <138> leaving <18>
Squares R2C3 and R2C9 in row 2 and R9C3 and R9C9 in row 9 form a Simple X-Wing pattern on possibility <7>. All other instances of this possibility in columns 3 and 9 can be removed.
R3C3 - removing <7> from <379> leaving <39>
R3C9 - removing <7> from <137> leaving <13>
R8C9 - removing <7> from <1378> leaving <138>
Squares R3C9<13>, R6C9<18> and R8C9<138> in column 9 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 column.
R9C9 - removing <3> from <237> leaving <27>
Squares R6C8, R6C9, R8C8 and R8C9 form a Type-1 Unique Rectangle on <18>.
R8C9 - removing <18> from <138> leaving <3>
R8C5 can only be <7>
R3C9 can only be <1>
R9C8 can only be <2>
R9C9 can only be <7>
R2C8 can only be <9>
R9C3 can only be <3>
R2C9 can only be <2>
R7C7 can only be <1>
R2C2 can only be <6>
R1C8 can only be <3>
R3C7 can only be <7>
R6C9 can only be <8>
R6C8 can only be <1>
R8C8 can only be <8>
R8C1 can only be <1>
R7C5 can only be <3>
R3C3 can only be <9>
R7C1 can only be <7>
R1C1 can only be <2>
R2C3 can only be <7>
R8C2 can only be <9>
R3C6 can only be <2>
R8C3 can only be <6>
R3C1 can only be <3>
R1C6 can only be <9>
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