Oct 31 - Super Hard
Puzzle Copyright © Kevin Stone
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Reasoning
R4C9 can only be <4>
R7C7 can only be <9>
R9C7 can only be <5>
R6C9 is the only square in row 6 that can be <5>
R8C8 is the only square in row 8 that can be <4>
R8C4 is the only square in row 8 that can be <5>
R5C7 is the only square in block 6 that can be <1>
Squares R1C7 and R3C7 in block 3 form a simple naked pair. These 2 squares both contain the 2 possibilities <48>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the block.
R1C8 - removing <8> from <278> leaving <27>
R2C8 - removing <8> from <2678> leaving <267>
Intersection of column 3 with block 1. The value <1> only appears in one or more of squares R1C3, R2C3 and R3C3 of column 3. 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 <1> from <12478> leaving <2478>
R2C1 - removing <1> from <12789> leaving <2789>
R2C2 - removing <1> from <124789> leaving <24789>
R3C1 - removing <1> from <178> leaving <78>
Intersection of column 9 with block 9. The value <3> only appears in one or more of squares R7C9, R8C9 and R9C9 of column 9. These squares are the ones that intersect with block 9. Thus, the other (non-intersecting) squares of block 9 cannot contain this value.
R9C8 - removing <3> from <236> leaving <26>
Intersection of row 9 with block 8. The value <3> only appears in one or more of squares R9C4, R9C5 and R9C6 of row 9. 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 <3> from <2367> leaving <267>
R8C5 - removing <3> from <2369> leaving <269>
R8C6 - removing <3> from <36> leaving <6>
Intersection of column 5 with block 5. The value <3> only appears in one or more of squares R4C5, R5C5 and R6C5 of column 5. These squares are the ones that intersect with block 5. Thus, the other (non-intersecting) squares of block 5 cannot contain this value.
R5C4 - removing <3> from <3469> leaving <469>
R5C6 - removing <3> from <38> leaving <8>
Squares R5C3 and R9C3 in column 3 and R5C4 and R9C4 in column 4 form a Simple X-Wing pattern on possibility <9>. All other instances of this possibility in rows 5 and 9 can be removed.
R5C2 - removing <9> from <269> leaving <26>
R9C2 - removing <9> from <2679> leaving <267>
R5C5 - removing <9> from <3469> leaving <346>
R5C8 - removing <9> from <39> leaving <3>
R6C5 is the only square in row 6 that can be <3>
Squares R1C2, R1C3 and R1C8 in row 1, R5C2 and R5C3 in row 5 and R9C2, R9C3 and R9C8 in row 9 form a Swordfish pattern on possibility <2>. All other instances of this possibility in columns 2, 3 and 8 can be removed.
R2C2 - removing <2> from <24789> leaving <4789>
R2C8 - removing <2> from <267> leaving <67>
R7C3 - removing <2> from <267> leaving <67>
R8C2 - removing <2> from <129> leaving <19>
Squares R2C8 (XY), R3C9 (XZ) and R2C6 (YZ) form an XY-Wing pattern on <1>. All squares that are buddies of both the XZ and YZ squares cannot be <1>.
R2C9 - removing <1> from <126> leaving <26>
R2C6 is the only square in row 2 that can be <1>
R1C3 is the only square in row 1 that can be <1>
R3C3 can only be <7>
R3C1 can only be <8>
R7C3 can only be <6>
R3C7 can only be <4>
R3C5 can only be <6>
R1C7 can only be <8>
R3C9 can only be <1>
R4C5 can only be <9>
R5C5 can only be <4>
R2C4 can only be <4>
R4C1 can only be <7>
R4C8 can only be <8>
R8C5 can only be <2>
R6C8 can only be <9>
R5C4 can only be <6>
R6C1 can only be <1>
R8C9 can only be <3>
R7C5 can only be <7>
R7C9 can only be <2>
R2C2 can only be <9>
R1C4 can only be <3>
R4C2 can only be <6>
R5C2 can only be <2>
R5C3 can only be <9>
R1C2 can only be <4>
R9C2 can only be <7>
R9C3 can only be <2>
R6C2 can only be <8>
R8C1 can only be <9>
R2C5 can only be <8>
R9C6 can only be <3>
R7C1 can only be <3>
R2C9 can only be <6>
R9C8 can only be <6>
R8C2 can only be <1>
R2C1 can only be <2>
R9C4 can only be <9>
R1C6 can only be <7>
R2C8 can only be <7>
R1C8 can only be <2>
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