Oct 23 - Very Hard
Puzzle Copyright © Kevin Stone
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Reasoning
R4C6 can only be <4>
R6C8 can only be <4>
R3C5 is the only square in row 3 that can be <3>
R1C8 is the only square in row 1 that can be <3>
R3C1 is the only square in row 3 that can be <4>
R4C8 is the only square in row 4 that can be <5>
R5C6 is the only square in row 5 that can be <1>
R6C4 is the only square in row 6 that can be <9>
Squares R5C7 and R5C9 in row 5 form a simple naked pair. These 2 squares both contain the 2 possibilities <28>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the row.
R5C1 - removing <2> from <2367> leaving <367>
R5C3 - removing <2> from <267> leaving <67>
R5C4 - removing <28> from <238> leaving <3>
R4C2 is the only square in row 4 that can be <3>
R9C1 is the only square in row 9 that can be <3>
R6C2 is the only square in block 4 that can be <2>
R8C1 is the only square in row 8 that can be <2>
Intersection of row 3 with block 3. The value <5> only appears in one or more of squares R3C7, R3C8 and R3C9 of row 3. These squares are the ones that intersect with block 3. Thus, the other (non-intersecting) squares of block 3 cannot contain this value.
R1C7 - removing <5> from <2569> leaving <269>
R1C9 - removing <5> from <2579> leaving <279>
R2C9 - removing <5> from <25789> leaving <2789>
Intersection of row 1 with block 1. The values <15> 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.
R2C1 - removing <5> from <5679> leaving <679>
R2C2 - removing <5> from <579> leaving <79>
Intersection of block 8 with row 8. The value <5> only appears in one or more of squares R8C4, R8C5 and R8C6 of block 8. These squares are the ones that intersect with row 8. Thus, the other (non-intersecting) squares of row 8 cannot contain this value.
R8C2 - removing <5> from <157> leaving <17>
R8C9 - removing <5> from <1578> leaving <178>
Squares R7C3<78>, R8C2<17> and R9C3<18> in block 7 form a comprehensive naked triplet. These 3 squares can only contain the 3 possibilities <178>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the block.
R7C1 - removing <7> from <579> leaving <59>
R9C2 - removing <1> from <159> leaving <59>
Squares R3C3 and R3C9 in row 3 and R7C3 and R7C9 in row 7 form a Simple X-Wing pattern on possibility <7>. All other instances of this possibility in columns 3 and 9 can be removed.
R1C3 - removing <7> from <1267> leaving <126>
R1C9 - removing <7> from <279> leaving <29>
R2C9 - removing <7> from <2789> leaving <289>
R5C3 - removing <7> from <67> leaving <6>
R8C9 - removing <7> from <178> leaving <18>
R5C1 can only be <7>
Squares R1C9<29>, R2C9<289> and R5C9<28> in column 9 form a comprehensive naked triplet. These 3 squares can only contain the 3 possibilities <289>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the column.
R3C9 - removing <2> from <257> leaving <57>
R7C9 - removing <89> from <45789> leaving <457>
R8C9 - removing <8> from <18> leaving <1>
R9C9 - removing <89> from <14589> leaving <145>
R8C2 can only be <7>
R2C2 can only be <9>
R7C3 can only be <8>
R2C1 can only be <6>
R9C2 can only be <5>
R7C5 can only be <4>
R9C3 can only be <1>
R9C9 can only be <4>
R1C2 can only be <1>
R7C1 can only be <9>
R1C3 can only be <2>
R1C5 can only be <7>
R1C9 can only be <9>
R3C3 can only be <7>
R6C5 can only be <6>
R2C6 can only be <5>
R1C7 can only be <6>
R1C1 can only be <5>
R2C4 can only be <2>
R8C6 can only be <6>
R3C9 can only be <5>
R3C7 can only be <2>
R7C9 can only be <7>
R6C6 can only be <7>
R9C5 can only be <8>
R7C7 can only be <5>
R8C8 can only be <8>
R8C4 can only be <5>
R2C8 can only be <7>
R9C8 can only be <6>
R4C5 can only be <2>
R9C7 can only be <9>
R2C9 can only be <8>
R4C4 can only be <8>
R5C9 can only be <2>
R5C7 can only be <8>
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