Jan 05 - Super Hard
Puzzle Copyright © Kevin Stone
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Reasoning
R2C6 is the only square in row 2 that can be <5>
R1C3 is the only square in row 1 that can be <5>
R4C7 is the only square in row 4 that can be <1>
R5C1 is the only square in row 5 that can be <9>
R5C3 is the only square in row 5 that can be <8>
R6C6 is the only square in row 6 that can be <9>
R9C9 is the only square in row 9 that can be <5>
R9C4 is the only square in row 9 that can be <9>
R8C9 is the only square in row 8 that can be <9>
R8C2 is the only square in row 8 that can be <6>
R8C3 is the only square in column 3 that can be <1>
R9C5 is the only square in row 9 that can be <1>
R1C4 is the only square in column 4 that can be <6>
R1C1 is the only square in row 1 that can be <1>
R2C4 is the only square in row 2 that can be <1>
R3C8 is the only square in row 3 that can be <6>
R3C5 is the only square in row 3 that can be <8>
R1C8 is the only square in row 1 that can be <8>
R9C7 is the only square in row 9 that can be <6>
R6C5 is the only square in row 6 that can be <6>
R5C9 is the only square in row 5 that can be <6>
R9C1 is the only square in row 9 that can be <8>
R8C4 is the only square in row 8 that can be <8>
R7C7 is the only square in row 7 that can be <8>
Intersection of column 1 with block 1. The value <3> only appears in one or more of squares R1C1, R2C1 and R3C1 of column 1. These squares are the ones that intersect with block 1. Thus, the other (non-intersecting) squares of block 1 cannot contain this value.
R1C2 - removing <3> from <2347> leaving <247>
R3C3 - removing <3> from <37> leaving <7>
R6C3 can only be <2>
R4C3 can only be <3>
R5C8 is the only square in row 5 that can be <3>
Intersection of row 2 with block 3. The value <7> only appears in one or more of squares R2C7, R2C8 and R2C9 of row 2. 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 <7> from <2347> leaving <234>
Intersection of column 6 with block 2. The value <4> only appears in one or more of squares R1C6, R2C6 and R3C6 of column 6. These squares are the ones that intersect with block 2. Thus, the other (non-intersecting) squares of block 2 cannot contain this value.
R1C5 - removing <4> from <347> leaving <37>
Intersection of column 6 with block 8. The value <2> only appears in one or more of squares R7C6, R8C6 and R9C6 of column 6. These squares are the ones that intersect with block 8. Thus, the other (non-intersecting) squares of block 8 cannot contain this value.
R7C5 - removing <2> from <2347> leaving <347>
Squares R1C2 and R1C9 in row 1 and R7C2 and R7C9 in row 7 form a Simple X-Wing pattern on possibility <2>. All other instances of this possibility in columns 2 and 9 can be removed.
R2C9 - removing <2> from <2347> leaving <347>
R4C9 - removing <2> from <247> leaving <47>
R9C2 - removing <2> from <237> leaving <37>
R4C5 is the only square in row 4 that can be <2>
R5C7 is the only square in row 5 that can be <2>
Squares R5C2 and R7C4 form a remote naked pair. <47> can be removed from any square that is common to their groups.
R7C2 - removing <7> from <237> leaving <23>
Squares R7C2 (XY), R7C9 (XZ) and R9C2 (YZ) form an XY-Wing pattern on <7>. All squares that are buddies of both the XZ and YZ squares cannot be <7>.
R9C8 - removing <7> from <27> leaving <2>
R2C8 can only be <7>
R7C9 can only be <7>
R2C7 can only be <4>
R7C4 can only be <4>
R4C9 can only be <4>
R2C9 can only be <3>
R6C7 can only be <7>
R2C1 can only be <2>
R1C9 can only be <2>
R4C4 can only be <7>
R6C1 can only be <4>
R7C5 can only be <3>
R7C2 can only be <2>
R1C5 can only be <7>
R9C6 can only be <7>
R9C2 can only be <3>
R8C6 can only be <2>
R5C5 can only be <4>
R1C2 can only be <4>
R8C1 can only be <7>
R5C2 can only be <7>
R3C1 can only be <3>
R1C6 can only be <3>
R3C6 can only be <4>
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