Aug 05 - Very Hard
Puzzle Copyright © Kevin Stone
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Reasoning
R1C6 can only be <2>
R5C9 can only be <8>
R1C7 is the only square in row 1 that can be <8>
R4C7 is the only square in row 4 that can be <4>
R8C1 is the only square in column 1 that can be <8>
R5C1 is the only square in column 1 that can be <9>
R4C5 is the only square in row 4 that can be <9>
R9C6 is the only square in column 6 that can be <6>
R9C5 is the only square in row 9 that can be <8>
R3C9 is the only square in column 9 that can be <4>
Squares R4C6 and R6C6 in block 5 form a simple naked pair. These 2 squares both contain the 2 possibilities <58>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the block.
R6C5 - removing <5> from <12357> leaving <1237>
Intersection of row 1 with block 1. The values <59> 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 these values.
R2C3 - removing <5> from <1235> leaving <123>
Intersection of column 1 with block 1. The value <3> only appears in one or more of squares R1C1, R2C1 and R3C1 of column 1. These squares are the ones that intersect with block 1. Thus, the other (non-intersecting) squares of block 1 cannot contain this value.
R1C3 - removing <3> from <1359> leaving <159>
R2C3 - removing <3> from <123> leaving <12>
R3C3 - removing <3> from <137> leaving <17>
Intersection of column 8 with block 6. The value <6> only appears in one or more of squares R4C8, R5C8 and R6C8 of column 8. These squares are the ones that intersect with block 6. Thus, the other (non-intersecting) squares of block 6 cannot contain this value.
R6C7 - removing <6> from <1367> leaving <137>
Squares R4C2<57>, R5C3<27> and R6C2<257> in block 4 form a comprehensive naked triplet. These 3 squares can only contain the 3 possibilities <257>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the block.
R4C3 - removing <57> from <5678> leaving <68>
R6C3 - removing <257> from <25678> leaving <68>
R1C3 is the only square in column 3 that can be <5>
R1C2 can only be <9>
Squares R7C1 and R9C2 in block 7 form a simple naked pair. These 2 squares both contain the 2 possibilities <27>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the block.
R7C3 - removing <27> from <247> leaving <4>
R8C3 - removing <7> from <379> leaving <39>
R9C3 - removing <27> from <23479> leaving <349>
R9C4 is the only square in row 9 that can be <4>
R1C5 is the only square in row 1 that can be <4>
Squares R7C5 and R8C5 in column 5 form a simple naked pair. These 2 squares both contain the 2 possibilities <57>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the column.
R5C5 - removing <7> from <127> leaving <12>
R6C5 - removing <7> from <1237> leaving <123>
Squares R1C4 and R6C4 in column 4 and R1C8 and R6C8 in column 8 form a Simple X-Wing pattern on possibility <1>. All other instances of this possibility in rows 1 and 6 can be removed.
R6C5 - removing <1> from <123> leaving <23>
R6C7 - removing <1> from <137> leaving <37>
Squares R1C4 and R1C8 in row 1 and R4C4 and R4C8 in row 4 form a Simple X-Wing pattern on possibility <3>. All other instances of this possibility in columns 4 and 8 can be removed.
R6C4 - removing <3> from <137> leaving <17>
R6C8 - removing <3> from <1367> leaving <167>
R9C8 - removing <3> from <37> leaving <7>
R9C2 can only be <2>
R7C1 can only be <7>
R7C5 can only be <5>
R3C1 can only be <3>
R7C9 can only be <6>
R8C5 can only be <7>
R7C7 can only be <2>
R2C1 can only be <2>
R2C3 can only be <1>
R3C3 can only be <7>
R5C3 can only be <2>
R5C5 can only be <1>
R5C7 can only be <7>
R3C5 can only be <6>
R6C4 can only be <7>
R6C7 can only be <3>
R6C2 can only be <5>
R4C4 can only be <3>
R6C5 can only be <2>
R9C7 can only be <9>
R4C8 can only be <6>
R9C3 can only be <3>
R8C7 can only be <5>
R3C7 can only be <1>
R2C5 can only be <3>
R1C8 can only be <3>
R1C4 can only be <1>
R4C3 can only be <8>
R6C8 can only be <1>
R6C6 can only be <8>
R4C2 can only be <7>
R6C3 can only be <6>
R4C6 can only be <5>
R8C9 can only be <3>
R2C7 can only be <6>
R8C3 can only be <9>
R2C9 can only be <5>
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