Oct 04 - Super Hard
Puzzle Copyright © Kevin Stone
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Reasoning
R9C5 can only be <7>
R2C8 is the only square in row 2 that can be <9>
R5C4 is the only square in row 5 that can be <7>
R6C4 is the only square in row 6 that can be <9>
R8C8 is the only square in row 8 that can be <2>
R1C8 is the only square in column 8 that can be <4>
Squares R2C4 and R2C9 in row 2 form a simple naked pair. These 2 squares both contain the 2 possibilities <13>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the row.
R2C2 - removing <3> from <234567> leaving <24567>
R2C6 - removing <3> from <356> leaving <56>
R2C7 - removing <13> from <1357> leaving <57>
Squares R6C8 and R9C8 in column 8 form a simple naked pair. These 2 squares both contain the 2 possibilities <68>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the column.
R4C8 - removing <68> from <1568> leaving <15>
R7C8 - removing <8> from <178> leaving <17>
Intersection of block 8 with row 8. The value <8> 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 <8> from <145678> leaving <14567>
R8C3 - removing <8> from <4568> leaving <456>
R8C7 - removing <8> from <1378> leaving <137>
Squares R2C4 and R8C4 in column 4 and R2C9 and R8C9 in column 9 form a Simple X-Wing pattern on possibility <3>. All other instances of this possibility in rows 2 and 8 can be removed.
R8C6 - removing <3> from <348> leaving <48>
R8C7 - removing <3> from <137> leaving <17>
R6C6 is the only square in column 6 that can be <3>
Squares R7C8 and R8C7 in block 9 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.
R7C7 - removing <17> from <1378> leaving <38>
R8C9 - removing <1> from <136> leaving <36>
Squares R7C3<48>, R7C5<34> and R7C7<38> in row 7 form a comprehensive naked triplet. These 3 squares can only contain the 3 possibilities <348>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the row.
R7C2 - removing <48> from <1478> leaving <17>
Squares R6C2 and R6C8 in row 6 and R9C2 and R9C8 in row 9 form a Simple X-Wing pattern on possibility <8>. All other instances of this possibility in columns 2 and 8 can be removed.
R4C2 - removing <8> from <268> leaving <26>
Intersection of row 4 with block 5. The value <8> only appears in one or more of squares R4C4, R4C5 and R4C6 of row 4. These squares are the ones that intersect with block 5. Thus, the other (non-intersecting) squares of block 5 cannot contain this value.
R5C6 - removing <8> from <4568> leaving <456>
Squares R5C6 (XYZ), R2C6 (XZ) and R6C5 (YZ) form an XYZ-Wing pattern on <6>. All squares that are buddies of all three squares cannot be <6>.
R4C6 - removing <6> from <568> leaving <58>
Squares R4C4<18>, R4C6<58> and R4C8<15> in row 4 form a comprehensive naked triplet. These 3 squares can only contain the 3 possibilities <158>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the row.
R4C5 - removing <15> from <1256> leaving <26>
Squares R4C2 and R4C5 in row 4, R6C2, R6C5 and R6C8 in row 6 and R9C2 and R9C8 in row 9 form a Swordfish pattern on possibility <6>. All other instances of this possibility in columns 2, 5 and 8 can be removed.
R2C2 - removing <6> from <24567> leaving <2457>
R3C2 - removing <6> from <3567> leaving <357>
R3C5 - removing <6> from <1356> leaving <135>
R5C5 - removing <6> from <12456> leaving <1245>
R8C2 - removing <6> from <14567> leaving <1457>
R3C3 is the only square in row 3 that can be <6>
R2C6 is the only square in row 2 that can be <6>
Intersection of column 6 with block 5. The value <5> 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 this value.
R5C5 - removing <5> from <1245> leaving <124>
Squares R6C2 (XYZ), R9C2 (XZ) and R5C1 (YZ) form an XYZ-Wing pattern on <6>. All squares that are buddies of all three squares cannot be <6>.
R4C2 - removing <6> from <26> leaving <2>
R4C5 can only be <6>
R6C5 can only be <4>
R7C5 can only be <3>
R5C6 can only be <5>
R7C7 can only be <8>
R1C5 can only be <5>
R8C4 can only be <8>
R7C3 can only be <4>
R9C8 can only be <6>
R8C6 can only be <4>
R4C4 can only be <1>
R8C3 can only be <5>
R9C2 can only be <8>
R6C8 can only be <8>
R8C9 can only be <3>
R1C2 can only be <3>
R3C5 can only be <1>
R5C5 can only be <2>
R2C4 can only be <3>
R4C8 can only be <5>
R4C6 can only be <8>
R3C8 can only be <7>
R5C7 can only be <1>
R5C9 can only be <6>
R8C7 can only be <7>
R5C1 can only be <4>
R6C2 can only be <6>
R5C3 can only be <8>
R2C3 can only be <2>
R8C1 can only be <6>
R8C2 can only be <1>
R2C7 can only be <5>
R7C8 can only be <1>
R2C9 can only be <1>
R3C7 can only be <3>
R3C2 can only be <5>
R2C1 can only be <7>
R7C2 can only be <7>
R2C2 can only be <4>
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