Sep 28 - Super Hard
Puzzle Copyright © Kevin Stone
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Reasoning
R3C3 is the only square in column 3 that can be <4>
R2C6 is the only square in column 6 that can be <8>
R5C3 is the only square in block 4 that can be <7>
R5C7 is the only square in block 6 that can be <3>
R5C4 can only be <4>
R4C8 is the only square in row 4 that can be <4>
R2C9 is the only square in row 2 that can be <4>
R8C5 is the only square in row 8 that can be <4>
R9C7 is the only square in row 9 that can be <4>
R6C5 is the only square in column 5 that can be <6>
R8C4 is the only square in column 4 that can be <6>
Squares R5C8 and R6C8 in column 8 form a simple naked pair. These 2 squares both contain the 2 possibilities <12>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the column.
R1C8 - removing <12> from <12789> leaving <789>
R2C8 - removing <12> from <12579> leaving <579>
R2C2 is the only square in row 2 that can be <2>
Intersection of row 1 with block 3. The values <27> only appears in one or more of squares R1C7, R1C8 and R1C9 of row 1. These squares are the ones that intersect with block 3. Thus, the other (non-intersecting) squares of block 3 cannot contain these values.
R2C8 - removing <7> from <579> leaving <59>
Intersection of column 1 with block 7. The values <37> only appears in one or more of squares R7C1, R8C1 and R9C1 of column 1. These squares are the ones that intersect with block 7. Thus, the other (non-intersecting) squares of block 7 cannot contain these values.
R8C2 - removing <3> from <3589> leaving <589>
R9C2 - removing <3> from <3568> leaving <568>
Intersection of column 3 with block 7. The value <5> only appears in one or more of squares R7C3, R8C3 and R9C3 of column 3. These squares are the ones that intersect with block 7. Thus, the other (non-intersecting) squares of block 7 cannot contain this value.
R7C1 - removing <5> from <1579> leaving <179>
R8C1 - removing <5> from <35789> leaving <3789>
R8C2 - removing <5> from <589> leaving <89>
R9C1 - removing <5> from <3578> leaving <378>
R9C2 - removing <5> from <568> leaving <68>
Intersection of column 6 with block 5. The values <12> only appears in one or more of squares R4C6, R5C6 and R6C6 of column 6. These squares are the ones that intersect with block 5. Thus, the other (non-intersecting) squares of block 5 cannot contain these values.
R4C5 - removing <1> from <159> leaving <59>
Intersection of column 7 with block 3. The value <8> only appears in one or more of squares R1C7, R2C7 and R3C7 of column 7. These squares are the ones that intersect with block 3. Thus, the other (non-intersecting) squares of block 3 cannot contain this value.
R1C8 - removing <8> from <789> leaving <79>
Intersection of block 4 with column 2. The values <135> only appears in one or more of squares R4C2, R5C2 and R6C2 of block 4. These squares are the ones that intersect with column 2. Thus, the other (non-intersecting) squares of column 2 cannot contain these values.
R1C2 - removing <1> from <1689> leaving <689>
Squares R5C8, R6C8, R5C6 and R6C6 form a Type-3 Unique Rectangle on <12>. Upon close inspection, it is clear that:
(R5C6 or R6C6)<57>, R6C4<37>, R4C5<59> and R4C4<39> form a naked quad on <3579> in block 5. No other squares in the block can contain these possibilities
R4C6 - removing <5> from <15> leaving <1>
Squares R3C9 (XY), R3C5 (XZ) and R2C8 (YZ) form an XY-Wing pattern on <9>. All squares that are buddies of both the XZ and YZ squares cannot be <9>.
R2C4 - removing <9> from <79> leaving <7>
R2C5 - removing <9> from <179> leaving <17>
R3C7 - removing <9> from <89> leaving <8>
R2C5 can only be <1>
R6C4 can only be <3>
R3C5 can only be <9>
R4C5 can only be <5>
R4C2 can only be <3>
R7C5 can only be <7>
R5C6 can only be <2>
R5C8 can only be <1>
R6C6 can only be <7>
R5C2 can only be <5>
R6C8 can only be <2>
R6C2 can only be <1>
R4C4 can only be <9>
R8C6 can only be <5>
Squares R2C1<59>, R3C1<15> and R7C1<19> in column 1 form a comprehensive naked triplet. These 3 squares can only contain the 3 possibilities <159>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the column.
R1C1 - removing <19> from <189> leaving <8>
R8C1 - removing <9> from <3789> leaving <378>
Squares R8C1 and R8C9 in row 8 form a simple naked pair. These 2 squares both contain the 2 possibilities <37>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the row.
R8C8 - removing <7> from <789> leaving <89>
Squares R8C1, R8C9, R9C1 and R9C9 form a Type-1 Unique Rectangle on <37>.
R9C9 - removing <37> from <357> leaving <5>
R9C3 can only be <6>
R3C9 can only be <1>
R7C9 can only be <2>
R3C1 can only be <5>
R7C7 can only be <9>
R1C9 can only be <7>
R9C2 can only be <8>
R1C3 can only be <1>
R7C3 can only be <5>
R1C8 can only be <9>
R8C9 can only be <3>
R2C1 can only be <9>
R7C1 can only be <1>
R1C7 can only be <2>
R8C8 can only be <8>
R8C2 can only be <9>
R9C8 can only be <7>
R8C1 can only be <7>
R9C1 can only be <3>
R1C2 can only be <6>
R2C8 can only be <5>
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