Jul 25 - Super Hard
Puzzle Copyright © Kevin Stone
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Reasoning
R4C2 can only be <9>
R9C1 can only be <8>
R4C6 can only be <1>
R4C5 can only be <4>
R2C6 is the only square in row 2 that can be <9>
R3C8 is the only square in row 3 that can be <9>
R5C5 is the only square in row 5 that can be <9>
R8C9 is the only square in row 8 that can be <2>
R8C1 is the only square in row 8 that can be <9>
R3C2 is the only square in column 2 that can be <8>
Squares R2C1 and R3C3 in block 1 form a simple naked pair. These 2 squares both contain the 2 possibilities <17>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the block.
R1C1 - removing <7> from <57> leaving <5>
R1C2 - removing <7> from <3457> leaving <345>
R2C3 - removing <17> from <1347> leaving <34>
Squares R1C2 and R9C2 in column 2 form a simple naked pair. These 2 squares both contain the 2 possibilities <34>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the column.
R7C2 - removing <3> from <357> leaving <57>
Intersection of column 8 with block 9. The value <1> only appears in one or more of squares R7C8, R8C8 and R9C8 of column 8. 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 <1> from <138> leaving <38>
Intersection of block 2 with column 5. The value <6> 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.
R6C5 - removing <6> from <3567> leaving <357>
R9C5 - removing <6> from <136> leaving <13>
Intersection of row 9 with block 9. The value <6> only appears in one or more of squares R9C7, R9C8 and R9C9 of row 9. These squares are the ones that intersect with block 9. Thus, the other (non-intersecting) squares of block 9 cannot contain this value.
R8C7 - removing <6> from <346> leaving <34>
Squares R1C2 and R1C5 in row 1 and R9C2 and R9C5 in row 9 form a Simple X-Wing pattern on possibility <3>. All other instances of this possibility in columns 2 and 5 can be removed.
R6C5 - removing <3> from <357> leaving <57>
R7C5 - removing <3> from <135> leaving <15>
Squares R6C2 and R6C5 in row 6 form a simple naked pair. These 2 squares both contain the 2 possibilities <57>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the row.
R6C4 - removing <7> from <2367> leaving <236>
R6C6 - removing <5> from <356> leaving <36>
Squares R1C2 and R9C2 in column 2 and R1C8 and R9C8 in column 8 form a Simple X-Wing pattern on possibility <4>. All other instances of this possibility in rows 1 and 9 can be removed.
R1C9 - removing <4> from <467> leaving <67>
R9C9 - removing <4> from <46> leaving <6>
R1C9 can only be <7>
Squares R5C3 and R5C6 in row 5 and R8C3 and R8C6 in row 8 form a Simple X-Wing pattern on possibility <5>. All other instances of this possibility in columns 3 and 6 can be removed.
R7C3 - removing <5> from <357> leaving <37>
Squares R2C1 and R5C1 in column 1 and R2C4 and R5C4 in column 4 form a Simple X-Wing pattern on possibility <7>. All other instances of this possibility in rows 2 and 5 can be removed.
R5C3 - removing <7> from <157> leaving <15>
Squares R9C8 (XY), R9C5 (XZ) and R8C7 (YZ) form an XY-Wing pattern on <3>. All squares that are buddies of both the XZ and YZ squares cannot be <3>.
R8C4 - removing <3> from <36> leaving <6>
R8C6 - removing <3> from <356> leaving <56>
R8C6 can only be <5>
R5C6 can only be <6>
R7C5 can only be <1>
R6C6 can only be <3>
R6C4 can only be <2>
R7C8 can only be <8>
R9C5 can only be <3>
R7C7 can only be <3>
R4C8 can only be <2>
R9C2 can only be <4>
R1C5 can only be <6>
R1C8 can only be <4>
R3C5 can only be <7>
R1C2 can only be <3>
R9C8 can only be <1>
R2C9 can only be <8>
R2C7 can only be <1>
R5C9 can only be <4>
R3C3 can only be <1>
R6C5 can only be <5>
R2C4 can only be <3>
R4C4 can only be <8>
R6C8 can only be <6>
R5C7 can only be <8>
R6C2 can only be <7>
R7C3 can only be <7>
R8C7 can only be <4>
R8C3 can only be <3>
R2C3 can only be <4>
R2C1 can only be <7>
R3C7 can only be <6>
R5C3 can only be <5>
R5C4 can only be <7>
R5C1 can only be <1>
R7C2 can only be <5>
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