Oct 12 - Super Hard
Puzzle Copyright © Kevin Stone
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Reasoning
R2C5 is the only square in row 2 that can be <3>
R2C3 is the only square in row 2 that can be <9>
R3C5 is the only square in row 3 that can be <9>
R4C2 is the only square in row 4 that can be <4>
R3C8 is the only square in row 3 that can be <4>
R1C1 is the only square in row 1 that can be <4>
R5C8 is the only square in row 5 that can be <3>
R5C5 is the only square in row 5 that can be <4>
R8C7 is the only square in row 8 that can be <4>
R7C4 is the only square in column 4 that can be <5>
R4C7 is the only square in column 7 that can be <5>
Squares R5C3, R5C4 and R5C6 in row 5 form a simple naked triplet. These 3 squares all contain the 3 possibilities <168>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the row.
R5C2 - removing <6> from <269> leaving <29>
R5C7 - removing <1> from <129> leaving <29>
Squares R7C1 and R8C1 in column 1 form a simple naked pair. These 2 squares both contain the 2 possibilities <78>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the column.
R2C1 - removing <7> from <127> leaving <12>
R6C1 - removing <78> from <1278> leaving <12>
Squares R7C1 and R8C1 in block 7 form a simple naked pair. These 2 squares both contain the 2 possibilities <78>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the block.
R7C2 - removing <7> from <367> leaving <36>
R8C2 - removing <7> from <3567> leaving <356>
R9C3 - removing <7> from <567> leaving <56>
Intersection of row 2 with block 3. The value <5> only appears in one or more of squares R2C7, R2C8 and R2C9 of row 2. These squares are the ones that intersect with block 3. Thus, the other (non-intersecting) squares of block 3 cannot contain this value.
R3C9 - removing <5> from <125> leaving <12>
Intersection of column 4 with block 2. The value <2> only appears in one or more of squares R1C4, R2C4 and R3C4 of column 4. These squares are the ones that intersect with block 2. Thus, the other (non-intersecting) squares of block 2 cannot contain this value.
R3C6 - removing <2> from <1278> leaving <178>
Intersection of column 5 with block 8. The value <8> only appears in one or more of squares R7C5, R8C5 and R9C5 of column 5. These squares are the ones that intersect with block 8. Thus, the other (non-intersecting) squares of block 8 cannot contain this value.
R7C6 - removing <8> from <123678> leaving <12367>
R8C6 - removing <8> from <3678> leaving <367>
Squares R5C2, R5C7, R6C2 and R6C7 form a Type-4 Unique Rectangle on <29>.
R6C2 - removing <2> from <2679> leaving <679>
R6C7 - removing <2> from <129> leaving <19>
Squares R7C1, R8C1, R7C5 and R8C5 form a Type-4 Unique Rectangle on <78>.
R7C5 - removing <7> from <1678> leaving <168>
R8C5 - removing <7> from <678> leaving <68>
Squares R6C1 (XY), R6C7 (XZ) and R5C2 (YZ) form an XY-Wing pattern on <9>. All squares that are buddies of both the XZ and YZ squares cannot be <9>.
R5C7 - removing <9> from <29> leaving <2>
R6C2 - removing <9> from <679> leaving <67>
R5C2 can only be <9>
R7C7 can only be <7>
R7C1 can only be <8>
R1C7 can only be <1>
R6C7 can only be <9>
R3C9 can only be <2>
R2C9 can only be <5>
R8C1 can only be <7>
R2C8 can only be <7>
R6C1 is the only square in row 6 that can be <2>
R2C1 can only be <1>
R2C4 can only be <2>
R1C2 is the only square in row 1 that can be <2>
R8C2 is the only square in row 8 that can be <5>
R3C2 can only be <7>
R9C3 can only be <6>
R9C5 can only be <7>
R9C9 can only be <3>
R7C2 can only be <3>
R1C5 can only be <6>
R9C6 can only be <2>
R8C9 can only be <6>
R1C4 can only be <7>
R7C5 can only be <1>
R8C5 can only be <8>
R3C3 can only be <5>
R6C2 can only be <6>
R6C8 can only be <8>
R4C8 can only be <6>
R8C6 can only be <3>
R4C9 can only be <1>
R7C8 can only be <2>
R9C8 can only be <5>
R7C6 can only be <6>
R4C4 can only be <8>
R4C3 can only be <7>
R3C4 can only be <1>
R5C6 can only be <1>
R5C3 can only be <8>
R5C4 can only be <6>
R3C6 can only be <8>
R6C6 can only be <7>
R6C3 can only be <1>
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