Sep 09 - Super Hard
Puzzle Copyright © Kevin Stone
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Reasoning
R2C9 is the only square in row 2 that can be <8>
R5C4 is the only square in row 5 that can be <2>
R6C5 is the only square in row 6 that can be <8>
R7C2 is the only square in row 7 that can be <8>
R8C8 is the only square in row 8 that can be <5>
R3C5 is the only square in block 2 that can be <5>
R2C2 is the only square in column 2 that can be <5>
Squares R1C4 and R1C6 in row 1 form a simple naked pair. These 2 squares both contain the 2 possibilities <47>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the row.
R1C1 - removing <47> from <3467> leaving <36>
R1C2 - removing <4> from <469> leaving <69>
R1C9 - removing <4> from <13469> leaving <1369>
Squares R5C3 and R5C6 in row 5 form a simple naked pair. These 2 squares both contain the 2 possibilities <46>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the row.
R5C5 - removing <4> from <134> leaving <13>
R5C7 - removing <6> from <136> leaving <13>
Squares R1C4 and R4C4 in column 4 form a simple naked pair. These 2 squares both contain the 2 possibilities <47>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the column.
R9C4 - removing <4> from <149> leaving <19>
Intersection of row 8 with block 9. The value <9> 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.
R9C9 - removing <9> from <1349> leaving <134>
Intersection of column 9 with block 9. The value <4> only appears in one or more of squares R7C9, R8C9 and R9C9 of column 9. These squares are the ones that intersect with block 9. Thus, the other (non-intersecting) squares of block 9 cannot contain this value.
R7C7 - removing <4> from <146> leaving <16>
R8C7 - removing <4> from <13469> leaving <1369>
Intersection of block 6 with column 9. The value <6> only appears in one or more of squares R4C9, R5C9 and R6C9 of block 6. These squares are the ones that intersect with column 9. Thus, the other (non-intersecting) squares of column 9 cannot contain this value.
R1C9 - removing <6> from <1369> leaving <139>
R8C9 - removing <6> from <13469> leaving <1349>
Squares R1C1<36>, R4C1<456>, R6C1<56> and R8C1<346> in column 1 form a comprehensive naked quad. These 4 squares can only contain the 4 possibilities <3456>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the column.
R2C1 - removing <46> from <2467> leaving <27>
R9C1 - removing <34> from <2347> leaving <27>
Intersection of row 9 with block 9. The value <3> only appears in one or more of squares R9C7, R9C8 and R9C9 of row 9. These squares are the ones that intersect with block 9. Thus, the other (non-intersecting) squares of block 9 cannot contain this value.
R8C7 - removing <3> from <1369> leaving <169>
R8C9 - removing <3> from <1349> leaving <149>
Squares R1C8 and R1C9 in row 1, R6C4 and R6C9 in row 6 and R9C4, R9C8 and R9C9 in row 9 form a Swordfish pattern on possibility <1>. All other instances of this possibility in columns 4, 8 and 9 can be removed.
R7C8 - removing <1> from <167> leaving <67>
R8C9 - removing <1> from <149> leaving <49>
Squares R1C4, R1C6, R4C4 and R4C6 form a Type-1 Unique Rectangle on <47>.
R4C6 - removing <47> from <4567> leaving <56>
R4C4 is the only square in row 4 that can be <7>
R1C4 can only be <4>
R1C6 can only be <7>
Squares R3C3 (XY), R1C1 (XZ) and R5C3 (YZ) form an XY-Wing pattern on <6>. All squares that are buddies of both the XZ and YZ squares cannot be <6>.
R2C3 - removing <6> from <467> leaving <47>
R4C1 - removing <6> from <456> leaving <45>
R6C1 - removing <6> from <56> leaving <5>
R4C1 can only be <4>
R4C5 can only be <3>
R5C3 can only be <6>
R4C9 can only be <6>
R5C5 can only be <1>
R4C6 can only be <5>
R6C9 can only be <1>
R5C6 can only be <4>
R5C7 can only be <3>
R7C5 can only be <4>
R6C4 can only be <9>
R9C6 can only be <9>
R6C6 can only be <6>
R9C4 can only be <1>
R1C8 is the only square in row 1 that can be <1>
Intersection of row 7 with block 9. The value <6> only appears in one or more of squares R7C7, R7C8 and R7C9 of row 7. These squares are the ones that intersect with block 9. Thus, the other (non-intersecting) squares of block 9 cannot contain this value.
R8C7 - removing <6> from <169> leaving <19>
Squares R3C7 (XY), R3C3 (XZ) and R1C9 (YZ) form an XY-Wing pattern on <3>. All squares that are buddies of both the XZ and YZ squares cannot be <3>.
R1C1 - removing <3> from <36> leaving <6>
R3C8 - removing <3> from <23> leaving <2>
R1C2 can only be <9>
R8C1 can only be <3>
R1C9 can only be <3>
R9C9 can only be <4>
R3C2 can only be <4>
R2C8 can only be <6>
R9C2 can only be <2>
R8C9 can only be <9>
R2C7 can only be <4>
R7C8 can only be <7>
R3C3 can only be <3>
R3C7 can only be <9>
R8C2 can only be <6>
R2C3 can only be <7>
R8C7 can only be <1>
R7C3 can only be <1>
R9C8 can only be <3>
R8C3 can only be <4>
R7C7 can only be <6>
R9C1 can only be <7>
R2C1 can only be <2>
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