Jan 07 - Super Hard
Puzzle Copyright © Kevin Stone
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Reasoning
R3C6 can only be <5>
R3C1 can only be <6>
R3C8 is the only square in row 3 that can be <2>
R4C7 is the only square in row 4 that can be <9>
R1C2 is the only square in row 1 that can be <9>
R3C9 is the only square in row 3 that can be <9>
R3C4 is the only square in row 3 that can be <3>
R7C8 is the only square in row 7 that can be <4>
R4C8 can only be <1>
R4C5 can only be <8>
R5C2 is the only square in row 5 that can be <8>
R9C5 is the only square in row 9 that can be <9>
R7C5 is the only square in column 5 that can be <2>
R5C7 is the only square in column 7 that can be <2>
R6C7 is the only square in column 7 that can be <4>
Squares R5C5 and R6C5 in column 5 form a simple naked pair. These 2 squares both contain the 2 possibilities <15>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the column.
R1C5 - removing <1> from <147> leaving <47>
Squares R1C5 and R3C5 in block 2 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 block.
R1C4 - removing <7> from <178> leaving <18>
Intersection of row 7 with block 7. The value <5> only appears in one or more of squares R7C1, R7C2 and R7C3 of row 7. These squares are the ones that intersect with block 7. Thus, the other (non-intersecting) squares of block 7 cannot contain this value.
R9C2 - removing <5> from <2567> leaving <267>
R9C3 - removing <5> from <23567> leaving <2367>
Intersection of column 7 with block 9. The value <6> 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.
R9C8 - removing <6> from <3567> leaving <357>
Intersection of block 1 with column 3. The value <5> only appears in one or more of squares R1C3, R2C3 and R3C3 of block 1. These squares are the ones that intersect with column 3. Thus, the other (non-intersecting) squares of column 3 cannot contain this value.
R5C3 - removing <5> from <1356> leaving <136>
R6C3 - removing <5> from <1356> leaving <136>
Squares R5C1 and R7C1 in column 1 and R5C9 and R7C9 in column 9 form a Simple X-Wing pattern on possibility <3>. All other instances of this possibility in rows 5 and 7 can be removed.
R5C3 - removing <3> from <136> leaving <16>
R5C8 - removing <3> from <367> leaving <67>
Squares R2C3 and R2C7 in row 2 and R8C3 and R8C7 in row 8 form a Simple X-Wing pattern on possibility <7>. All other instances of this possibility in columns 3 and 7 can be removed.
R1C3 - removing <7> from <457> leaving <45>
R1C7 - removing <7> from <357> leaving <35>
R9C3 - removing <7> from <2367> leaving <236>
R9C7 - removing <7> from <3567> leaving <356>
Squares R5C3 (XY), R5C5 (XZ) and R6C2 (YZ) form an XY-Wing pattern on <5>. All squares that are buddies of both the XZ and YZ squares cannot be <5>.
R6C5 - removing <5> from <15> leaving <1>
R5C1 - removing <5> from <35> leaving <3>
R5C9 can only be <7>
R7C1 can only be <5>
R5C8 can only be <6>
R7C9 can only be <3>
R6C3 can only be <6>
R5C5 can only be <5>
R5C3 can only be <1>
R6C8 can only be <3>
R6C2 can only be <5>
R8C3 can only be <7>
R8C7 can only be <6>
R2C3 can only be <5>
R7C2 can only be <6>
R9C7 can only be <5>
R9C8 can only be <7>
R1C7 can only be <3>
R2C7 can only be <7>
R9C4 can only be <8>
R1C8 can only be <5>
R1C3 can only be <4>
R7C6 can only be <1>
R9C2 can only be <2>
R7C4 can only be <7>
R1C6 can only be <8>
R9C3 can only be <3>
R4C2 can only be <4>
R9C6 can only be <6>
R1C4 can only be <1>
R1C5 can only be <7>
R4C3 can only be <2>
R3C2 can only be <7>
R3C5 can only be <4>
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