Sep 27 - Super Hard
Puzzle Copyright © Kevin Stone
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Reasoning
R1C5 is the only square in row 1 that can be <7>
R1C1 is the only square in row 1 that can be <9>
R9C9 is the only square in row 9 that can be <7>
R2C8 is the only square in column 8 that can be <8>
R8C8 is the only square in block 9 that can be <9>
R8C4 can only be <3>
R6C8 can only be <7>
R2C4 can only be <4>
R5C2 is the only square in row 5 that can be <7>
R4C2 is the only square in column 2 that can be <2>
R4C8 can only be <3>
R5C8 can only be <2>
R6C2 is the only square in column 2 that can be <4>
Squares R1C6, R2C5 and R2C6 in block 2 form a simple naked triplet. These 3 squares all contain the 3 possibilities <135>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the block.
R3C5 - removing <5> from <258> leaving <28>
Squares R8C2 and R9C3 in block 7 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 block.
R7C1 - removing <1> from <134> leaving <34>
R9C1 - removing <15> from <1345> leaving <34>
Intersection of row 2 with block 2. The value <3> only appears in one or more of squares R2C4, R2C5 and R2C6 of row 2. These squares are the ones that intersect with block 2. Thus, the other (non-intersecting) squares of block 2 cannot contain this value.
R1C6 - removing <3> from <135> leaving <15>
Intersection of column 1 with block 4. The values <16> only appears in one or more of squares R4C1, R5C1 and R6C1 of column 1. These squares are the ones that intersect with block 4. Thus, the other (non-intersecting) squares of block 4 cannot contain these values.
R5C3 - removing <1> from <158> leaving <58>
Squares R7C5<14>, R8C5<156>, R8C6<156> and R9C6<145> in block 8 form a comprehensive naked quad. These 4 squares can only contain the 4 possibilities <1456>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the block.
R9C5 - removing <145> from <12459> leaving <29>
Squares R3C1 and R3C9 in row 3 and R6C1 and R6C9 in row 6 form a Simple X-Wing pattern on possibility <5>. All other instances of this possibility in columns 1 and 9 can be removed.
R1C9 - removing <5> from <235> leaving <23>
R5C1 - removing <5> from <1568> leaving <168>
R5C9 - removing <5> from <1459> leaving <149>
Squares R2C2 and R8C2 in column 2 and R2C5 and R8C5 in column 5 form a Simple X-Wing pattern on possibility <5>. All other instances of this possibility in rows 2 and 8 can be removed.
R2C6 - removing <5> from <135> leaving <13>
R8C6 - removing <5> from <156> leaving <16>
Squares R3C1 and R3C5 in row 3 and R4C1 and R4C5 in row 4 form a Simple X-Wing pattern on possibility <8>. All other instances of this possibility in columns 1 and 5 can be removed.
R5C1 - removing <8> from <168> leaving <16>
R5C5 - removing <8> from <34689> leaving <3469>
Squares R1C7 (XY), R9C7 (XZ) and R1C6 (YZ) form an XY-Wing pattern on <1>. All squares that are buddies of both the XZ and YZ squares cannot be <1>.
R9C6 - removing <1> from <145> leaving <45>
Squares R5C1 (XY), R5C7 (XZ) and R6C1 (YZ) form an XY-Wing pattern on <5>. All squares that are buddies of both the XZ and YZ squares cannot be <5>.
R6C9 - removing <5> from <59> leaving <9>
R5C3 - removing <5> from <58> leaving <8>
R5C4 can only be <9>
R4C1 can only be <1>
R9C4 can only be <2>
R6C5 can only be <6>
R6C1 can only be <5>
R9C5 can only be <9>
R1C4 can only be <8>
R3C5 can only be <2>
R3C9 can only be <5>
R3C1 can only be <8>
R1C7 can only be <3>
R4C9 can only be <4>
R5C1 can only be <6>
R4C5 can only be <8>
R5C9 can only be <1>
R5C7 can only be <5>
R7C9 can only be <3>
R7C1 can only be <4>
R1C9 can only be <2>
R9C7 can only be <1>
R9C3 can only be <5>
R7C5 can only be <1>
R9C1 can only be <3>
R8C5 can only be <5>
R8C6 can only be <6>
R8C2 can only be <1>
R2C5 can only be <3>
R9C6 can only be <4>
R1C3 can only be <1>
R5C6 can only be <3>
R1C6 can only be <5>
R2C2 can only be <5>
R2C6 can only be <1>
R5C5 can only be <4>
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