Oct 26 - Super Hard
Puzzle Copyright © Kevin Stone
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Reasoning
R1C4 is the only square in row 1 that can be <9>
R3C9 is the only square in row 3 that can be <6>
R3C8 is the only square in row 3 that can be <9>
R7C1 is the only square in row 7 that can be <6>
Intersection of column 9 with block 9. The value <5> 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 <5> from <578> leaving <78>
R8C7 - removing <5> from <457> leaving <47>
Intersection of block 4 with column 2. The value <3> 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 this value.
R3C2 - removing <3> from <1358> leaving <158>
R7C2 - removing <3> from <12357> leaving <1257>
R8C2 - removing <3> from <12357> leaving <1257>
Squares R1C1 and R1C9 in row 1 and R5C1 and R5C9 in row 5 form a Simple X-Wing pattern on possibility <7>. All other instances of this possibility in columns 1 and 9 can be removed.
R7C9 - removing <7> from <1578> leaving <158>
R9C1 - removing <7> from <1357> leaving <135>
R9C9 - removing <7> from <157> leaving <15>
R9C6 is the only square in row 9 that can be <7>
Squares R3C3, R7C3 and R8C3 in column 3, R3C5 and R7C5 in column 5 and R7C8 and R8C8 in column 8 form a Swordfish pattern on possibility <3>. All other instances of this possibility in rows 3, 7 and 8 can be removed.
R3C1 - removing <3> from <135> leaving <15>
R8C4 - removing <3> from <1235> leaving <125>
R8C6 - removing <3> from <135> leaving <15>
Squares R1C1 (XY), R3C3 (XZ) and R5C1 (YZ) form an XY-Wing pattern on <1>. All squares that are buddies of both the XZ and YZ squares cannot be <1>.
R3C1 - removing <1> from <15> leaving <5>
R2C7 is the only square in row 2 that can be <5>
Intersection of column 7 with block 9. The value <7> only appears in one or more of squares R7C7, R8C7 and R9C7 of column 7. These squares are the ones that intersect with block 9. Thus, the other (non-intersecting) squares of block 9 cannot contain this value.
R7C8 - removing <7> from <1378> leaving <138>
R8C8 - removing <7> from <1347> leaving <134>
Squares R3C5 (XY), R1C6 (XZ) and R3C7 (YZ) form an XY-Wing pattern on <8>. All squares that are buddies of both the XZ and YZ squares cannot be <8>.
R1C9 - removing <8> from <78> leaving <7>
R1C1 can only be <3>
R1C6 can only be <8>
R9C1 can only be <1>
R3C3 can only be <1>
R2C4 can only be <6>
R2C6 can only be <4>
R2C8 can only be <8>
R5C6 can only be <1>
R3C5 can only be <3>
R6C8 can only be <1>
R3C7 can only be <4>
R3C2 can only be <8>
R7C5 can only be <2>
R8C7 can only be <7>
R5C1 can only be <7>
R5C9 can only be <8>
R8C6 can only be <5>
R5C4 can only be <2>
R6C2 can only be <3>
R4C8 can only be <7>
R7C8 can only be <3>
R5C5 can only be <4>
R7C3 can only be <7>
R8C8 can only be <4>
R8C4 can only be <1>
R4C6 can only be <3>
R7C7 can only be <8>
R9C4 can only be <3>
R9C9 can only be <5>
R8C2 can only be <2>
R4C4 can only be <5>
R6C4 can only be <8>
R7C9 can only be <1>
R6C6 can only be <6>
R4C2 can only be <1>
R7C2 can only be <5>
R2C3 can only be <2>
R8C3 can only be <3>
R2C2 can only be <7>
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