Aug 26 - Very Hard
Puzzle Copyright © Kevin Stone
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Reasoning
R7C8 is the only square in row 7 that can be <1>
R9C5 is the only square in row 9 that can be <5>
R5C1 is the only square in column 1 that can be <6>
R8C8 is the only square in column 8 that can be <6>
R4C9 is the only square in column 9 that can be <4>
R6C2 is the only square in row 6 that can be <4>
R8C7 is the only square in row 8 that can be <4>
R1C5 is the only square in row 1 that can be <4>
R2C8 is the only square in row 2 that can be <4>
R2C2 is the only square in row 2 that can be <8>
R2C3 is the only square in row 2 that can be <2>
R3C8 is the only square in row 3 that can be <2>
R7C3 is the only square in row 7 that can be <4>
R5C2 is the only square in column 2 that can be <2>
R3C3 is the only square in column 3 that can be <1>
R5C9 is the only square in column 9 that can be <3>
Squares R4C3 and R4C8 in row 4 form a simple naked pair. These 2 squares both contain the 2 possibilities <79>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the row.
R4C4 - removing <9> from <3569> leaving <356>
R4C5 - removing <9> from <369> leaving <36>
R4C6 - removing <9> from <569> leaving <56>
Intersection of row 1 with block 1. The value <9> only appears in one or more of squares R1C1, R1C2 and R1C3 of row 1. These squares are the ones that intersect with block 1. Thus, the other (non-intersecting) squares of block 1 cannot contain this value.
R3C2 - removing <9> from <579> leaving <57>
Intersection of row 2 with block 2. The values <157> only appears in one or more of squares R2C4, R2C5 and R2C6 of row 2. These squares are the ones that intersect with block 2. Thus, the other (non-intersecting) squares of block 2 cannot contain these values.
R3C4 - removing <5> from <569> leaving <69>
R3C5 - removing <7> from <679> leaving <69>
Squares R4C3 and R9C3 in column 3 and R4C8 and R9C8 in column 8 form a Simple X-Wing pattern on possibility <7>. All other instances of this possibility in rows 4 and 9 can be removed.
R9C9 - removing <7> from <78> leaving <8>
R3C9 can only be <7>
R3C2 can only be <5>
R1C7 can only be <5>
R3C7 can only be <8>
R6C5 is the only square in row 6 that can be <8>
R5C5 can only be <9>
R5C8 can only be <8>
R3C5 can only be <6>
R6C4 can only be <1>
R6C6 can only be <2>
R2C4 can only be <5>
R2C6 can only be <7>
R2C5 can only be <1>
R8C6 can only be <9>
R3C4 can only be <9>
R4C5 can only be <3>
R4C4 can only be <6>
R7C5 can only be <7>
R7C7 can only be <9>
R8C5 can only be <2>
R7C1 can only be <5>
R7C2 can only be <3>
R7C6 can only be <6>
R6C7 can only be <7>
R9C8 can only be <7>
R8C4 can only be <3>
R9C3 can only be <9>
R4C8 can only be <9>
R4C6 can only be <5>
R4C3 can only be <7>
R6C1 can only be <9>
R8C2 can only be <7>
R1C2 can only be <9>
R1C1 can only be <7>
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