Jan 02 - Super Hard
Puzzle Copyright © Kevin Stone
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Reasoning
R2C8 can only be <3>
R6C9 can only be <9>
R6C1 can only be <5>
R4C9 can only be <3>
R4C7 can only be <7>
R5C9 can only be <8>
R2C3 is the only square in row 2 that can be <7>
R3C4 is the only square in row 3 that can be <7>
R3C3 is the only square in row 3 that can be <8>
R5C5 is the only square in row 5 that can be <5>
R7C3 is the only square in row 7 that can be <1>
R7C1 is the only square in row 7 that can be <7>
R3C8 is the only square in column 8 that can be <1>
R3C7 is the only square in row 3 that can be <9>
Squares R5C7 and R6C7 in column 7 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 column.
R7C7 - removing <2> from <23458> leaving <3458>
R8C7 - removing <2> from <234> leaving <34>
R8C8 is the only square in row 8 that can be <2>
R7C8 can only be <9>
R8C3 is the only square in row 8 that can be <9>
Intersection of column 2 with block 1. The value <6> only appears in one or more of squares R1C2, R2C2 and R3C2 of column 2. These squares are the ones that intersect with block 1. Thus, the other (non-intersecting) squares of block 1 cannot contain this value.
R1C3 - removing <6> from <3456> leaving <345>
Intersection of block 5 with column 5. The value <6> only appears in one or more of squares R4C5, R5C5 and R6C5 of block 5. These squares are the ones that intersect with column 5. Thus, the other (non-intersecting) squares of column 5 cannot contain this value.
R1C5 - removing <6> from <1346> leaving <134>
R3C5 - removing <6> from <2346> leaving <234>
R7C5 - removing <6> from <2346> leaving <234>
Squares R2C2 and R2C7 in row 2 and R8C2 and R8C7 in row 8 form a Simple X-Wing pattern on possibility <4>. All other instances of this possibility in columns 2 and 7 can be removed.
R1C7 - removing <4> from <456> leaving <56>
R3C2 - removing <4> from <3456> leaving <356>
R7C2 - removing <4> from <345> leaving <35>
R7C7 - removing <4> from <3458> leaving <358>
R9C7 - removing <4> from <3458> leaving <358>
Squares R1C3 and R1C7 in row 1 and R9C3 and R9C7 in row 9 form a Simple X-Wing pattern on possibility <5>. All other instances of this possibility in columns 3 and 7 can be removed.
R7C7 - removing <5> from <358> leaving <38>
Squares R1C7 (XY), R3C9 (XZ) and R1C4 (YZ) form an XY-Wing pattern on <4>. All squares that are buddies of both the XZ and YZ squares cannot be <4>.
R3C5 - removing <4> from <234> leaving <23>
R3C6 - removing <4> from <2346> leaving <236>
Intersection of block 2 with row 1. The values <14> only appears in one or more of squares R1C4, R1C5 and R1C6 of block 2. These squares are the ones that intersect with row 1. Thus, the other (non-intersecting) squares of row 1 cannot contain these values.
R1C3 - removing <4> from <345> leaving <35>
Squares R3C1 (XY), R1C3 (XZ) and R3C9 (YZ) form an XY-Wing pattern on <5>. All squares that are buddies of both the XZ and YZ squares cannot be <5>.
R3C2 - removing <5> from <356> leaving <36>
R1C7 - removing <5> from <56> leaving <6>
R1C4 can only be <4>
R2C7 can only be <4>
R2C2 can only be <6>
R8C7 can only be <3>
R3C9 can only be <5>
R7C9 can only be <4>
R8C2 can only be <4>
R7C7 can only be <8>
R5C4 can only be <9>
R3C2 can only be <3>
R3C1 can only be <4>
R3C5 can only be <2>
R7C2 can only be <5>
R1C3 can only be <5>
R3C6 can only be <6>
R7C5 can only be <3>
R9C4 can only be <8>
R7C6 can only be <2>
R1C5 can only be <1>
R9C6 can only be <4>
R7C4 can only be <6>
R9C7 can only be <5>
R9C3 can only be <3>
R9C5 can only be <9>
R5C6 can only be <1>
R1C6 can only be <3>
R6C5 can only be <6>
R4C1 can only be <9>
R5C1 can only be <3>
R5C7 can only be <2>
R5C3 can only be <4>
R6C7 can only be <1>
R6C3 can only be <2>
R4C5 can only be <4>
R4C3 can only be <6>
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