Jul 26 - Super Hard
Puzzle Copyright © Kevin Stone
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Reasoning
R5C5 can only be <2>
R6C2 can only be <6>
R5C3 can only be <1>
R5C7 can only be <6>
R4C2 can only be <3>
R1C6 is the only square in row 1 that can be <6>
R4C7 is the only square in row 4 that can be <9>
R7C1 is the only square in row 7 that can be <6>
Squares R2C6 and R2C7 in row 2 and R8C6 and R8C7 in row 8 form a Simple X-Wing pattern on possibility <1>. All other instances of this possibility in columns 6 and 7 can be removed.
R1C7 - removing <1> from <137> leaving <37>
R3C6 - removing <1> from <1249> leaving <249>
R7C6 - removing <1> from <1289> leaving <289>
R9C6 - removing <1> from <12489> leaving <2489>
R9C7 - removing <1> from <123> leaving <23>
Squares R1C1 and R1C9 in row 1 and R9C1 and R9C9 in row 9 form a Simple X-Wing pattern on possibility <1>. All other instances of this possibility in columns 1 and 9 can be removed.
R3C1 - removing <1> from <137> leaving <37>
R3C9 - removing <1> from <1345> leaving <345>
R4C9 - removing <1> from <1258> leaving <258>
R7C9 - removing <1> from <1238> leaving <238>
R4C8 is the only square in row 4 that can be <1>
Squares R2C6 (XY), R3C5 (XZ) and R2C3 (YZ) form an XY-Wing pattern on <3>. All squares that are buddies of both the XZ and YZ squares cannot be <3>.
R2C4 - removing <3> from <345> leaving <45>
R3C1 - removing <3> from <37> leaving <7>
R3C8 can only be <4>
R6C8 can only be <8>
R7C8 can only be <7>
R1C7 is the only square in row 1 that can be <7>
R4C3 is the only square in row 4 that can be <8>
R6C9 is the only square in row 6 that can be <4>
R6C3 is the only square in row 6 that can be <7>
R8C4 is the only square in row 8 that can be <7>
Squares R1C1 and R1C9 in row 1 form a simple naked pair. These 2 squares both contain the 2 possibilities <13>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the row.
R1C3 - removing <3> from <349> leaving <49>
R1C4 - removing <3> from <349> leaving <49>
Squares R4C1 and R6C1 in column 1 form a simple naked pair. These 2 squares both contain the 2 possibilities <25>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the column.
R9C1 - removing <2> from <123> leaving <13>
Intersection of block 2 with row 3. The values <23> only appears in one or more of squares R3C4, R3C5 and R3C6 of block 2. These squares are the ones that intersect with row 3. Thus, the other (non-intersecting) squares of row 3 cannot contain these values.
R3C9 - removing <3> from <35> leaving <5>
R4C9 can only be <2>
R4C1 can only be <5>
R6C7 can only be <5>
R6C1 can only be <2>
R2C4 is the only square in row 2 that can be <5>
Intersection of row 7 with block 8. The value <2> only appears in one or more of squares R7C4, R7C5 and R7C6 of row 7. These squares are the ones that intersect with block 8. Thus, the other (non-intersecting) squares of block 8 cannot contain this value.
R8C6 - removing <2> from <12> leaving <1>
R9C4 - removing <2> from <2349> leaving <349>
R9C6 - removing <2> from <2489> leaving <489>
R2C6 can only be <4>
R7C5 can only be <3>
R2C3 can only be <3>
R1C4 can only be <9>
R7C9 can only be <8>
R3C5 can only be <1>
R1C3 can only be <4>
R7C4 can only be <2>
R9C4 can only be <4>
R3C6 can only be <2>
R2C7 can only be <1>
R8C3 can only be <2>
R1C1 can only be <1>
R1C9 can only be <3>
R3C2 can only be <9>
R3C4 can only be <3>
R7C6 can only be <9>
R7C2 can only be <1>
R9C6 can only be <8>
R8C7 can only be <3>
R9C3 can only be <9>
R9C7 can only be <2>
R9C9 can only be <1>
R9C1 can only be <3>
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