Jul 03 - Very Hard
Puzzle Copyright © Kevin Stone
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Reasoning
R4C5 can only be <3>
R8C5 can only be <2>
R6C5 can only be <6>
R2C5 can only be <1>
R1C6 is the only square in row 1 that can be <4>
R5C8 is the only square in row 5 that can be <1>
R7C8 is the only square in row 7 that can be <4>
R3C6 is the only square in column 6 that can be <5>
Squares R1C4 and R3C4 in column 4 form a simple naked pair. These 2 squares both contain the 2 possibilities <69>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the column.
R7C4 - removing <9> from <179> leaving <17>
R9C4 - removing <9> from <179> leaving <17>
Squares R4C8 and R6C7 in block 6 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 block.
R4C7 - removing <79> from <479> leaving <4>
R6C8 - removing <79> from <3789> leaving <38>
R5C7 can only be <2>
R5C2 is the only square in row 5 that can be <4>
Intersection of row 7 with block 7. The value <6> only appears in one or more of squares R7C1, R7C2 and R7C3 of row 7. These squares are the ones that intersect with block 7. Thus, the other (non-intersecting) squares of block 7 cannot contain this value.
R9C1 - removing <6> from <35678> leaving <3578>
R9C2 - removing <6> from <135678> leaving <13578>
R9C3 - removing <6> from <13567> leaving <1357>
Squares R2C2 and R2C8 in row 2 and R8C2 and R8C8 in row 8 form a Simple X-Wing pattern on possibility <7>. All other instances of this possibility in columns 2 and 8 can be removed.
R1C2 - removing <7> from <123567> leaving <12356>
R1C8 - removing <7> from <23679> leaving <2369>
R4C2 - removing <7> from <579> leaving <59>
R4C8 - removing <7> from <79> leaving <9>
R6C2 - removing <7> from <3789> leaving <389>
R7C2 - removing <7> from <1678> leaving <168>
R9C2 - removing <7> from <13578> leaving <1358>
R9C8 - removing <7> from <25679> leaving <2569>
R4C2 can only be <5>
R6C7 can only be <7>
R6C3 can only be <3>
R4C3 can only be <7>
R8C2 can only be <7>
R6C8 can only be <8>
R5C3 can only be <6>
R6C2 can only be <9>
R5C9 can only be <3>
R8C8 can only be <5>
R2C2 can only be <6>
R2C8 can only be <7>
R3C1 can only be <3>
R3C2 can only be <2>
R3C8 can only be <6>
R1C2 can only be <1>
R3C4 can only be <9>
R9C8 can only be <2>
R1C7 can only be <9>
R5C1 can only be <8>
R1C8 can only be <3>
R1C3 can only be <5>
R7C2 can only be <8>
R1C1 can only be <7>
R9C3 can only be <1>
R1C4 can only be <6>
R1C9 can only be <2>
R9C7 can only be <6>
R3C9 can only be <8>
R7C1 can only be <6>
R9C1 can only be <5>
R7C6 can only be <9>
R9C2 can only be <3>
R7C9 can only be <7>
R9C6 can only be <8>
R7C4 can only be <1>
R9C9 can only be <9>
R9C4 can only be <7>
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