Jan 17 - Super Hard
Puzzle Copyright © Kevin Stone
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Reasoning
R4C7 can only be <7>
R5C4 can only be <2>
R5C5 can only be <5>
R7C4 can only be <8>
R4C5 can only be <8>
R6C7 can only be <5>
R5C6 can only be <1>
R6C5 can only be <7>
R6C6 can only be <6>
R6C3 can only be <9>
R9C7 can only be <8>
R7C6 can only be <5>
R3C4 can only be <4>
R3C6 can only be <8>
R4C4 can only be <9>
R4C6 can only be <4>
R4C3 can only be <6>
R6C4 can only be <3>
R1C3 can only be <8>
R2C7 is the only square in row 2 that can be <4>
R2C8 is the only square in row 2 that can be <8>
R7C3 is the only square in row 7 that can be <4>
R8C2 is the only square in row 8 that can be <8>
Squares R2C9 and R8C9 in column 9 form a simple naked pair. These 2 squares both contain the 2 possibilities <35>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the column.
R3C9 - removing <35> from <3579> leaving <79>
Intersection of row 2 with block 1. The values <12> only appears in one or more of squares R2C1, R2C2 and R2C3 of row 2. These squares are the ones that intersect with block 1. Thus, the other (non-intersecting) squares of block 1 cannot contain these values.
R3C2 - removing <2> from <25679> leaving <5679>
R3C3 - removing <2> from <235> leaving <35>
Squares R3C3 and R9C3 in column 3 form a simple naked pair. These 2 squares both contain the 2 possibilities <35>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the column.
R2C3 - removing <35> from <1235> leaving <12>
R8C3 - removing <35> from <1235> leaving <12>
Intersection of row 8 with block 9. The value <5> only appears in one or more of squares R8C7, R8C8 and R8C9 of row 8. These squares are the ones that intersect with block 9. Thus, the other (non-intersecting) squares of block 9 cannot contain this value.
R9C8 - removing <5> from <357> leaving <37>
Squares R1C7<69>, R1C8<67> and R3C9<79> in block 3 form a comprehensive naked triplet. These 3 squares can only contain the 3 possibilities <679>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the block.
R3C7 - removing <69> from <269> leaving <2>
R3C8 - removing <67> from <23567> leaving <235>
Squares R3C3 and R3C8 in row 3 form a simple naked pair. These 2 squares both contain the 2 possibilities <35>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the row.
R3C1 - removing <3> from <367> leaving <67>
R3C2 - removing <5> from <5679> leaving <679>
Intersection of row 3 with block 1. The value <6> only appears in one or more of squares R3C1, R3C2 and R3C3 of row 3. These squares are the ones that intersect with block 1. Thus, the other (non-intersecting) squares of block 1 cannot contain this value.
R1C2 - removing <6> from <679> leaving <79>
Squares R3C3 and R3C8 in row 3 and R9C3 and R9C8 in row 9 form a Simple X-Wing pattern on possibility <3>. All other instances of this possibility in columns 3 and 8 can be removed.
R8C8 - removing <3> from <2356> leaving <256>
Squares R1C2 and R1C8 in row 1 and R9C2 and R9C8 in row 9 form a Simple X-Wing pattern on possibility <7>. All other instances of this possibility in columns 2 and 8 can be removed.
R3C2 - removing <7> from <679> leaving <69>
R7C2 - removing <7> from <267> leaving <26>
R7C8 - removing <7> from <267> leaving <26>
Squares R7C2 and R7C8 in row 7 form a simple naked pair. These 2 squares both contain the 2 possibilities <26>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the row.
R7C1 - removing <6> from <167> leaving <17>
R7C7 - removing <6> from <169> leaving <19>
Squares R8C3 (XY), R8C7 (XZ) and R7C2 (YZ) form an XY-Wing pattern on <6>. All squares that are buddies of both the XZ and YZ squares cannot be <6>.
R7C8 - removing <6> from <26> leaving <2>
R8C1 - removing <6> from <136> leaving <13>
R7C2 can only be <6>
R3C2 can only be <9>
R3C9 can only be <7>
R1C2 can only be <7>
R3C1 can only be <6>
R7C9 can only be <9>
R1C8 can only be <6>
R7C7 can only be <1>
R9C2 can only be <5>
R1C7 can only be <9>
R8C8 can only be <5>
R7C1 can only be <7>
R8C7 can only be <6>
R8C9 can only be <3>
R3C8 can only be <3>
R8C1 can only be <1>
R2C9 can only be <5>
R9C8 can only be <7>
R9C3 can only be <3>
R2C2 can only be <2>
R3C3 can only be <5>
R2C3 can only be <1>
R2C1 can only be <3>
R8C3 can only be <2>
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