Jul 16 - Very Hard
Puzzle Copyright © Kevin Stone
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Reasoning
R8C8 can only be <5>
R2C8 can only be <9>
R7C7 can only be <6>
R9C9 can only be <2>
Squares R1C1 and R9C1 in column 1 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.
R4C1 - removing <7> from <237> leaving <23>
R5C1 - removing <5> from <2356> leaving <236>
R6C1 - removing <5> from <2356> leaving <236>
Squares R6C3 and R7C3 in column 3 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 column.
R3C3 - removing <5> from <157> leaving <17>
R4C3 - removing <8> from <178> leaving <17>
Intersection of block 5 with row 5. The values <29> only appears in one or more of squares R5C4, R5C5 and R5C6 of block 5. These squares are the ones that intersect with row 5. Thus, the other (non-intersecting) squares of row 5 cannot contain these values.
R5C1 - removing <2> from <236> leaving <36>
R5C2 - removing <9> from <1589> leaving <158>
R5C8 - removing <2> from <28> leaving <8>
R5C5 can only be <3>
R5C1 can only be <6>
R6C9 is the only square in row 6 that can be <6>
R6C1 is the only square in row 6 that can be <3>
R4C1 can only be <2>
R4C8 can only be <4>
R4C5 can only be <8>
R6C8 can only be <2>
R6C5 can only be <4>
R4C9 is the only square in row 4 that can be <3>
Squares R9C1 and R9C5 in row 9 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 row.
R9C4 - removing <5> from <459> leaving <49>
R9C6 - removing <7> from <479> leaving <49>
Squares R2C2 and R5C2 in column 2 form a simple naked pair. These 2 squares both contain the 2 possibilities <15>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the column.
R4C2 - removing <1> from <179> leaving <79>
R6C2 - removing <5> from <589> leaving <89>
Squares R1C1<57>, R1C5<157> and R1C9<15> in row 1 form a comprehensive naked triplet. These 3 squares can only contain the 3 possibilities <157>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the row.
R1C4 - removing <15> from <1358> leaving <38>
R1C6 - removing <7> from <378> leaving <38>
Squares R1C6 and R7C6 in column 6 form a simple naked pair. These 2 squares both contain the 2 possibilities <38>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the column.
R8C6 - removing <8> from <678> leaving <67>
Squares R3C3 and R4C3 in column 3 and R3C7 and R4C7 in column 7 form a Simple X-Wing pattern on possibility <1>. All other instances of this possibility in rows 3 and 4 can be removed.
R3C4 - removing <1> from <125> leaving <25>
Squares R1C1 and R1C5 in row 1 and R9C1 and R9C5 in row 9 form a Simple X-Wing pattern on possibility <7>. All other instances of this possibility in columns 1 and 5 can be removed.
R8C5 - removing <7> from <167> leaving <16>
Squares R3C4 and R3C7 in row 3, R6C3 and R6C7 in row 6 and R7C3 and R7C4 in row 7 form a Swordfish pattern on possibility <5>. All other instances of this possibility in columns 3, 4 and 7 can be removed.
R2C4 - removing <5> from <145> leaving <14>
Squares R1C9 and R2C2 form a remote naked pair. <15> can be removed from any square that is common to their groups.
R1C1 - removing <5> from <57> leaving <7>
R9C1 can only be <5>
R3C3 can only be <1>
R3C7 can only be <5>
R4C3 can only be <7>
R2C2 can only be <5>
R3C4 can only be <2>
R6C7 can only be <9>
R1C9 can only be <1>
R4C2 can only be <9>
R6C2 can only be <8>
R4C7 can only be <1>
R9C5 can only be <7>
R7C3 can only be <8>
R8C6 can only be <6>
R1C5 can only be <5>
R5C9 can only be <5>
R5C2 can only be <1>
R3C6 can only be <7>
R5C4 can only be <9>
R5C6 can only be <2>
R9C4 can only be <4>
R6C3 can only be <5>
R8C2 can only be <7>
R7C6 can only be <3>
R7C4 can only be <5>
R1C6 can only be <8>
R8C5 can only be <1>
R2C6 can only be <4>
R9C6 can only be <9>
R2C4 can only be <1>
R1C4 can only be <3>
R2C5 can only be <6>
R8C4 can only be <8>
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