Oct 14 - Super Hard
Puzzle Copyright © Kevin Stone
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Reasoning
R3C2 can only be <5>
R7C4 is the only square in row 7 that can be <8>
R7C2 is the only square in row 7 that can be <2>
R7C3 is the only square in row 7 that can be <3>
R7C7 is the only square in row 7 that can be <5>
R8C9 is the only square in row 8 that can be <7>
R1C9 can only be <1>
R7C9 can only be <9>
R7C8 can only be <1>
R8C8 can only be <4>
R9C7 can only be <6>
R5C9 is the only square in row 5 that can be <6>
R6C3 is the only square in row 6 that can be <9>
R3C1 is the only square in row 3 that can be <9>
R5C8 is the only square in row 5 that can be <9>
R9C1 is the only square in row 9 that can be <4>
R3C3 is the only square in column 3 that can be <6>
Squares R8C1 and R8C3 in row 8 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 row.
R8C4 - removing <15> from <125> leaving <2>
R8C5 - removing <5> from <2356> leaving <236>
R8C6 - removing <15> from <12356> leaving <236>
Intersection of row 1 with block 2. The values <25> only appears in one or more of squares R1C4, R1C5 and R1C6 of row 1. These squares are the ones that intersect with block 2. Thus, the other (non-intersecting) squares of block 2 cannot contain these values.
R3C6 - removing <2> from <278> leaving <78>
Intersection of row 6 with block 5. The value <5> only appears in one or more of squares R6C4, R6C5 and R6C6 of row 6. These squares are the ones that intersect with block 5. Thus, the other (non-intersecting) squares of block 5 cannot contain this value.
R5C4 - removing <5> from <157> leaving <17>
R5C6 - removing <5> from <123578> leaving <12378>
Squares R4C4 and R5C4 in column 4 form a simple naked pair. These 2 squares both contain the 2 possibilities <17>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the column.
R1C4 - removing <7> from <457> leaving <45>
R2C4 - removing <7> from <479> leaving <49>
R9C4 - removing <1> from <159> leaving <59>
R9C6 is the only square in row 9 that can be <1>
Squares R4C4 and R5C4 in block 5 form a simple naked pair. These 2 squares both contain the 2 possibilities <17>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the block.
R5C6 - removing <7> from <2378> leaving <238>
Squares R6C5<358>, R6C6<358> and R6C9<38> in row 6 form a comprehensive naked triplet. These 3 squares can only contain the 3 possibilities <358>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the row.
R6C2 - removing <3> from <134> leaving <14>
R6C7 - removing <3> from <134> leaving <14>
R5C2 is the only square in column 2 that can be <3>
Squares R8C1, R8C3, R5C1 and R5C3 form a Type-4 Unique Rectangle on <15>.
R5C1 - removing <1> from <1578> leaving <578>
R5C3 - removing <1> from <157> leaving <57>
Squares R3C6 (XY), R3C7 (XZ) and R5C6 (YZ) form an XY-Wing pattern on <2>. All squares that are buddies of both the XZ and YZ squares cannot be <2>.
R5C7 - removing <2> from <12> leaving <1>
R5C4 can only be <7>
R6C7 can only be <4>
R6C2 can only be <1>
R5C3 can only be <5>
R4C4 can only be <1>
R2C2 can only be <4>
R2C4 can only be <9>
R1C3 can only be <7>
R9C4 can only be <5>
R5C1 can only be <8>
R8C3 can only be <1>
R8C1 can only be <5>
R9C5 can only be <9>
R1C4 can only be <4>
R4C3 can only be <4>
R2C1 can only be <1>
R5C6 can only be <2>
R4C1 can only be <7>
R1C6 can only be <5>
R1C5 can only be <2>
R6C5 is the only square in row 6 that can be <5>
Squares R2C9 and R4C5 form a remote naked pair. <38> can be removed from any square that is common to their groups.
R2C5 - removing <8> from <68> leaving <6>
R8C5 can only be <3>
R8C6 can only be <6>
R4C5 can only be <8>
R4C8 can only be <2>
R6C6 can only be <3>
R4C7 can only be <3>
R3C8 can only be <8>
R6C9 can only be <8>
R2C9 can only be <3>
R2C7 can only be <7>
R3C6 can only be <7>
R2C6 can only be <8>
R3C7 can only be <2>
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