Sep 01 - Super Hard
Puzzle Copyright © Kevin Stone
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Reasoning
R4C7 can only be <8>
R5C5 can only be <2>
R6C1 can only be <2>
R5C8 can only be <5>
R5C2 can only be <8>
R4C1 can only be <1>
R4C8 is the only square in row 4 that can be <2>
R4C2 is the only square in row 4 that can be <3>
Intersection of row 7 with block 8. The value <8> only appears in one or more of squares R7C4, R7C5 and R7C6 of row 7. These squares are the ones that intersect with block 8. Thus, the other (non-intersecting) squares of block 8 cannot contain this value.
R8C4 - removing <8> from <24568> leaving <2456>
R8C6 - removing <8> from <12578> leaving <1257>
Intersection of block 1 with row 2. The value <8> only appears in one or more of squares R2C1, R2C2 and R2C3 of block 1. These squares are the ones that intersect with row 2. Thus, the other (non-intersecting) squares of row 2 cannot contain this value.
R2C4 - removing <8> from <23458> leaving <2345>
R2C6 - removing <8> from <25789> leaving <2579>
R2C8 - removing <8> from <13468> leaving <1346>
Squares R7C8<47>, R8C7<147> and R9C8<147> in block 9 form a comprehensive naked triplet. These 3 squares can only contain the 3 possibilities <147>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the block.
R8C8 - removing <147> from <13479> leaving <39>
R8C9 - removing <4> from <349> leaving <39>
Squares R2C1 and R8C1 in column 1 and R2C5 and R8C5 in column 5 form a Simple X-Wing pattern on possibility <7>. All other instances of this possibility in rows 2 and 8 can be removed.
R2C2 - removing <7> from <1279> leaving <129>
R8C2 - removing <7> from <4567> leaving <456>
R2C6 - removing <7> from <2579> leaving <259>
R8C6 - removing <7> from <1257> leaving <125>
R8C7 - removing <7> from <147> leaving <14>
R6C7 is the only square in column 7 that can be <7>
Squares R2C5 and R8C5 in column 5 and R2C7 and R8C7 in column 7 form a Simple X-Wing pattern on possibility <4>. All other instances of this possibility in rows 2 and 8 can be removed.
R8C2 - removing <4> from <456> leaving <56>
R2C4 - removing <4> from <2345> leaving <235>
R8C4 - removing <4> from <2456> leaving <256>
R2C8 - removing <4> from <1346> leaving <136>
R2C9 - removing <4> from <346> leaving <36>
R6C9 is the only square in column 9 that can be <4>
Squares R8C5 (XY), R8C7 (XZ) and R9C6 (YZ) form an XY-Wing pattern on <1>. All squares that are buddies of both the XZ and YZ squares cannot be <1>.
R9C8 - removing <1> from <147> leaving <47>
R8C6 - removing <1> from <125> leaving <25>
R8C7 is the only square in row 8 that can be <1>
R2C7 can only be <4>
R2C5 can only be <7>
R2C1 can only be <8>
R8C5 can only be <4>
R9C4 can only be <6>
R2C3 can only be <9>
R8C1 can only be <7>
R4C3 can only be <6>
R3C2 can only be <1>
R3C8 can only be <8>
R2C2 can only be <2>
R3C4 can only be <4>
R3C6 can only be <9>
R1C8 can only be <3>
R4C9 can only be <9>
R6C3 can only be <5>
R8C9 can only be <3>
R6C8 can only be <6>
R6C2 can only be <9>
R8C3 can only be <8>
R9C2 can only be <4>
R8C8 can only be <9>
R2C9 can only be <6>
R9C8 can only be <7>
R7C2 can only be <5>
R9C6 can only be <1>
R7C8 can only be <4>
R2C8 can only be <1>
R2C6 can only be <5>
R1C2 can only be <7>
R2C4 can only be <3>
R8C6 can only be <2>
R7C4 can only be <8>
R8C2 can only be <6>
R7C6 can only be <7>
R1C4 can only be <2>
R8C4 can only be <5>
R1C6 can only be <8>
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