Jan 03 - Super Hard
Puzzle Copyright © Kevin Stone
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Reasoning
R3C7 is the only square in row 3 that can be <7>
R3C5 is the only square in row 3 that can be <5>
R3C1 is the only square in row 3 that can be <1>
R2C4 is the only square in row 2 that can be <1>
R4C5 is the only square in row 4 that can be <1>
R5C7 is the only square in row 5 that can be <1>
R8C2 is the only square in row 8 that can be <1>
R8C7 is the only square in row 8 that can be <3>
R6C1 is the only square in column 1 that can be <8>
R8C6 is the only square in column 6 that can be <7>
R8C1 can only be <9>
R8C8 is the only square in row 8 that can be <8>
R2C9 is the only square in row 2 that can be <8>
R7C5 is the only square in row 7 that can be <8>
R5C6 is the only square in row 5 that can be <8>
Squares R1C5 and R9C5 in column 5 form a simple naked pair. These 2 squares both contain the 2 possibilities <69>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the column.
R5C5 - removing <69> from <3469> leaving <34>
R6C5 - removing <69> from <3469> leaving <34>
Squares R5C5 and R6C5 in block 5 form a simple naked pair. These 2 squares both contain the 2 possibilities <34>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the block.
R5C4 - removing <4> from <2469> leaving <269>
R6C6 - removing <4> from <2469> leaving <269>
Intersection of column 4 with block 5. The value <2> only appears in one or more of squares R4C4, R5C4 and R6C4 of column 4. These squares are the ones that intersect with block 5. Thus, the other (non-intersecting) squares of block 5 cannot contain this value.
R6C6 - removing <2> from <269> leaving <69>
Intersection of row 6 with block 6. The value <2> only appears in one or more of squares R6C7, R6C8 and R6C9 of row 6. These squares are the ones that intersect with block 6. Thus, the other (non-intersecting) squares of block 6 cannot contain this value.
R4C8 - removing <2> from <269> leaving <69>
R4C9 - removing <2> from <2369> leaving <369>
R5C8 - removing <2> from <2469> leaving <469>
R2C8 is the only square in column 8 that can be <2>
R1C6 is the only square in row 1 that can be <2>
Intersection of block 3 with row 3. The value <9> only appears in one or more of squares R3C7, R3C8 and R3C9 of block 3. These squares are the ones that intersect with row 3. Thus, the other (non-intersecting) squares of row 3 cannot contain this value.
R3C6 - removing <9> from <469> leaving <46>
Squares R8C3, R8C4, R7C3 and R7C4 form a Type-4 Unique Rectangle on <46>.
R7C3 - removing <6> from <24567> leaving <2457>
R7C4 - removing <6> from <456> leaving <45>
Squares R4C1, R7C1, R4C3 and R7C3 form a Type-4 Unique Rectangle on <27>.
R4C3 - removing <2> from <23679> leaving <3679>
R7C3 - removing <2> from <2457> leaving <457>
Squares R7C2 (XY), R7C4 (XZ) and R8C3 (YZ) form an XY-Wing pattern on <4>. All squares that are buddies of both the XZ and YZ squares cannot be <4>.
R8C4 - removing <4> from <46> leaving <6>
R7C3 - removing <4> from <457> leaving <57>
R8C3 can only be <4>
R9C5 can only be <9>
R9C4 can only be <5>
R1C5 can only be <6>
R1C7 can only be <5>
R3C6 can only be <4>
R1C3 can only be <9>
R2C7 can only be <4>
R2C6 can only be <9>
R7C4 can only be <4>
R6C6 can only be <6>
R6C7 can only be <2>
R9C7 can only be <6>
R9C3 can only be <2>
R7C9 can only be <2>
R7C1 can only be <7>
R7C3 can only be <5>
R4C1 can only be <2>
R7C2 can only be <6>
R2C3 can only be <3>
R2C2 can only be <5>
R5C3 can only be <6>
R4C4 can only be <9>
R4C8 can only be <6>
R5C4 can only be <2>
R4C3 can only be <7>
R4C9 can only be <3>
R3C8 can only be <9>
R6C9 can only be <9>
R6C2 can only be <3>
R3C9 can only be <6>
R5C8 can only be <4>
R5C5 can only be <3>
R6C5 can only be <4>
R5C2 can only be <9>
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