Dec 01 - Super Hard
Puzzle Copyright © Kevin Stone
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Reasoning
R2C6 is the only square in row 2 that can be <4>
R1C9 is the only square in row 1 that can be <4>
R4C1 is the only square in row 4 that can be <4>
R7C5 is the only square in row 7 that can be <5>
R9C3 is the only square in row 9 that can be <4>
R6C4 is the only square in column 4 that can be <2>
R5C5 is the only square in column 5 that can be <7>
R6C6 is the only square in block 5 that can be <3>
Squares R4C4 and R4C6 in row 4 form a simple naked pair. These 2 squares both contain the 2 possibilities <59>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the row.
R4C8 - removing <5> from <5678> leaving <678>
R6C8 is the only square in column 8 that can be <5>
Squares R5C7 and R5C9 in row 5 form a simple naked pair. These 2 squares both contain the 2 possibilities <12>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the row.
R5C3 - removing <1> from <135> leaving <35>
R7C3 is the only square in column 3 that can be <1>
R8C6 is the only square in row 8 that can be <1>
R6C2 is the only square in column 2 that can be <1>
Squares R7C7 and R8C8 in block 9 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 block.
R7C9 - removing <68> from <368> leaving <3>
R9C7 - removing <68> from <1678> leaving <17>
R9C9 - removing <68> from <13678> leaving <137>
Intersection of row 3 with block 1. The value <5> only appears in one or more of squares R3C1, R3C2 and R3C3 of row 3. These squares are the ones that intersect with block 1. Thus, the other (non-intersecting) squares of block 1 cannot contain this value.
R1C1 - removing <5> from <35679> leaving <3679>
R1C3 - removing <5> from <356> leaving <36>
Intersection of column 3 with block 1. The value <6> only appears in one or more of squares R1C3, R2C3 and R3C3 of column 3. These squares are the ones that intersect with block 1. Thus, the other (non-intersecting) squares of block 1 cannot contain this value.
R1C1 - removing <6> from <3679> leaving <379>
R3C1 - removing <6> from <569> leaving <59>
Squares R2C2 and R2C4 in row 2 and R8C2 and R8C4 in row 8 form a Simple X-Wing pattern on possibility <3>. All other instances of this possibility in columns 2 and 4 can be removed.
R1C4 - removing <3> from <35689> leaving <5689>
R9C4 - removing <3> from <3689> leaving <689>
Squares R2C4 and R2C8 in row 2 and R8C4 and R8C8 in row 8 form a Simple X-Wing pattern on possibility <6>. All other instances of this possibility in columns 4 and 8 can be removed.
R1C4 - removing <6> from <5689> leaving <589>
R4C8 - removing <6> from <678> leaving <78>
R9C4 - removing <6> from <689> leaving <89>
R4C9 is the only square in row 4 that can be <6>
Squares R1C4<589>, R4C4<59> and R9C4<89> in column 4 form a comprehensive naked triplet. These 3 squares can only contain the 3 possibilities <589>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the column.
R8C4 - removing <8> from <368> leaving <36>
Intersection of block 8 with row 9. The values <89> only appears in one or more of squares R9C4, R9C5 and R9C6 of block 8. These squares are the ones that intersect with row 9. Thus, the other (non-intersecting) squares of row 9 cannot contain these values.
R9C1 - removing <8> from <368> leaving <36>
Squares R4C4, R4C6, R1C4 and R1C6 form a Type-4 Unique Rectangle on <59>.
R1C4 - removing <9> from <589> leaving <58>
R1C6 - removing <9> from <569> leaving <56>
Intersection of block 2 with column 5. The value <9> only appears in one or more of squares R1C5, R2C5 and R3C5 of block 2. These squares are the ones that intersect with column 5. Thus, the other (non-intersecting) squares of column 5 cannot contain this value.
R9C5 - removing <9> from <389> leaving <38>
Squares R2C2 (XY), R1C3 (XZ) and R2C8 (YZ) form an XY-Wing pattern on <6>. All squares that are buddies of both the XZ and YZ squares cannot be <6>.
R1C7 - removing <6> from <678> leaving <78>
Squares R1C7 (XY), R2C8 (XZ) and R7C7 (YZ) form an XY-Wing pattern on <6>. All squares that are buddies of both the XZ and YZ squares cannot be <6>.
R3C7 - removing <6> from <268> leaving <28>
R8C8 - removing <6> from <68> leaving <8>
R8C2 can only be <3>
R4C8 can only be <7>
R7C7 can only be <6>
R4C2 can only be <8>
R2C8 can only be <6>
R6C9 can only be <8>
R6C1 can only be <7>
R3C9 can only be <2>
R7C1 can only be <8>
R8C4 can only be <6>
R2C2 can only be <7>
R9C1 can only be <6>
R2C4 can only be <3>
R9C6 can only be <9>
R9C4 can only be <8>
R4C6 can only be <5>
R3C7 can only be <8>
R5C9 can only be <1>
R4C4 can only be <9>
R1C6 can only be <6>
R5C7 can only be <2>
R9C9 can only be <7>
R9C5 can only be <3>
R1C4 can only be <5>
R9C7 can only be <1>
R1C3 can only be <3>
R3C5 can only be <9>
R1C7 can only be <7>
R1C1 can only be <9>
R5C3 can only be <5>
R3C1 can only be <5>
R1C5 can only be <8>
R5C1 can only be <3>
R3C3 can only be <6>
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