Aug 12 - Super Hard
Puzzle Copyright © Kevin Stone
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Reasoning
R1C4 can only be <8>
R4C4 can only be <5>
R4C6 can only be <2>
R6C6 can only be <6>
R8C5 can only be <9>
R9C6 can only be <4>
R1C5 can only be <4>
R1C6 can only be <7>
R2C5 can only be <5>
R2C3 can only be <3>
R4C9 can only be <7>
R6C4 can only be <9>
R4C1 can only be <4>
R9C4 can only be <3>
R5C5 can only be <8>
R9C5 can only be <1>
R2C7 can only be <7>
R7C9 is the only square in row 7 that can be <8>
R8C2 is the only square in row 8 that can be <7>
R5C1 is the only square in row 5 that can be <7>
Intersection of row 8 with block 9. The value <3> only appears in one or more of squares R8C7, R8C8 and R8C9 of row 8. These squares are the ones that intersect with block 9. Thus, the other (non-intersecting) squares of block 9 cannot contain this value.
R7C8 - removing <3> from <369> leaving <69>
Intersection of column 3 with block 7. The value <5> only appears in one or more of squares R7C3, R8C3 and R9C3 of column 3. These squares are the ones that intersect with block 7. Thus, the other (non-intersecting) squares of block 7 cannot contain this value.
R9C1 - removing <5> from <2569> leaving <269>
Intersection of column 7 with block 9. The value <5> 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.
R9C9 - removing <5> from <2569> leaving <269>
Squares R1C1 and R1C9 in row 1 and R9C1 and R9C9 in row 9 form a Simple X-Wing pattern on possibility <6>. All other instances of this possibility in columns 1 and 9 can be removed.
R7C1 - removing <6> from <369> leaving <39>
Squares R1C3 and R9C3 in column 3 and R1C7 and R9C7 in column 7 form a Simple X-Wing pattern on possibility <9>. All other instances of this possibility in rows 1 and 9 can be removed.
R1C1 - removing <9> from <269> leaving <26>
R9C1 - removing <9> from <269> leaving <26>
R1C9 - removing <9> from <2369> leaving <236>
R9C9 - removing <9> from <269> leaving <26>
Squares R9C1 and R9C9 in row 9 form a simple naked pair. These 2 squares both contain the 2 possibilities <26>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the row.
R9C3 - removing <2> from <259> leaving <59>
Squares R1C1 and R9C1 in column 1 form a simple naked pair. These 2 squares both contain the 2 possibilities <26>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the column.
R3C1 - removing <2> from <259> leaving <59>
Intersection of row 3 with block 3. The value <2> only appears in one or more of squares R3C7, R3C8 and R3C9 of row 3. These squares are the ones that intersect with block 3. Thus, the other (non-intersecting) squares of block 3 cannot contain this value.
R1C9 - removing <2> from <236> leaving <36>
Squares R7C8 (XY), R7C2 (XZ) and R5C8 (YZ) form an XY-Wing pattern on <3>. All squares that are buddies of both the XZ and YZ squares cannot be <3>.
R5C2 - removing <3> from <35> leaving <5>
R3C2 can only be <4>
R6C1 can only be <3>
R6C9 can only be <5>
R7C1 can only be <9>
R7C8 can only be <6>
R3C1 can only be <5>
R9C3 can only be <5>
R7C2 can only be <3>
R2C8 can only be <4>
R9C9 can only be <2>
R9C7 can only be <9>
R8C3 can only be <2>
R1C7 can only be <3>
R9C1 can only be <6>
R3C9 can only be <9>
R8C8 can only be <3>
R1C9 can only be <6>
R8C7 can only be <5>
R1C1 can only be <2>
R2C2 can only be <6>
R3C8 can only be <2>
R5C9 can only be <3>
R5C8 can only be <9>
R1C3 can only be <9>
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