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Dec 02 - Super Hard
Puzzle Copyright © Kevin Stone
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Reasoning
R5C5 can only be <7>
R6C9 can only be <3>
R4C8 can only be <5>
R4C9 can only be <6>
R4C1 can only be <3>
R4C2 can only be <9>
R2C9 is the only square in row 2 that can be <1>
R3C8 is the only square in row 3 that can be <9>
R5C2 is the only square in row 5 that can be <5>
R5C3 is the only square in row 5 that can be <6>
R6C8 is the only square in row 6 that can be <8>
R7C8 is the only square in row 7 that can be <1>
R7C1 is the only square in row 7 that can be <6>
R8C7 is the only square in row 8 that can be <9>
R9C4 is the only square in row 9 that can be <6>
Squares R7C5 and R8C4 in block 8 form a simple naked pair. These 2 squares both contain the 2 possibilities <23>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the block.
R8C5 - removing <23> from <2358> leaving <58>
R8C4 is the only square in row 8 that can be <3>
R7C5 can only be <2>
R7C9 can only be <7>
R7C2 can only be <3>
R2C5 is the only square in column 5 that can be <3>
Intersection of row 3 with block 1. The value <4> only appears in one or more of squares R3C1, R3C2 and R3C3 of row 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 <4> from <247> leaving <27>
R1C3 - removing <4> from <479> leaving <79>
R2C1 - removing <4> from <245> leaving <25>
R2C3 - removing <4> from <489> leaving <89>
R8C3 is the only square in column 3 that can be <4>
Intersection of row 8 with block 8. The value <8> only appears in one or more of squares R8C4, R8C5 and R8C6 of row 8. These squares are the ones that intersect with block 8. Thus, the other (non-intersecting) squares of block 8 cannot contain this value.
R9C6 - removing <8> from <578> leaving <57>
Squares R1C2<27>, R1C3<79> and R1C4<29> in row 1 form a comprehensive naked triplet. These 3 squares can only contain the 3 possibilities <279>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the row.
R1C7 - removing <2> from <2345> leaving <345>
R1C8 - removing <2> from <234> leaving <34>
Squares R1C6 and R1C7 in row 1 and R9C6 and R9C7 in row 9 form a Simple X-Wing pattern on possibility <5>. All other instances of this possibility in columns 6 and 7 can be removed.
R2C6 - removing <5> from <458> leaving <48>
R2C7 - removing <5> from <245> leaving <24>
R8C6 - removing <5> from <578> leaving <78>
R2C1 is the only square in row 2 that can be <5>
Squares R2C7 and R5C7 in column 7 form a simple naked pair. These 2 squares both contain the 2 possibilities <24>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the column.
R1C7 - removing <4> from <345> leaving <35>
R9C7 - removing <2> from <235> leaving <35>
Squares R3C1 and R8C1 in column 1 and R3C9 and R8C9 in column 9 form a Simple X-Wing pattern on possibility <2>. All other instances of this possibility in rows 3 and 8 can be removed.
R3C2 - removing <2> from <248> leaving <48>
Squares R1C2 (XY), R3C1 (XZ) and R6C2 (YZ) form an XY-Wing pattern on <4>. All squares that are buddies of both the XZ and YZ squares cannot be <4>.
R6C1 - removing <4> from <47> leaving <7>
R3C2 - removing <4> from <48> leaving <8>
R3C5 can only be <5>
R2C3 can only be <9>
R3C9 can only be <2>
R8C5 can only be <8>
R1C6 can only be <4>
R3C1 can only be <4>
R8C9 can only be <5>
R2C7 can only be <4>
R6C2 can only be <4>
R8C1 can only be <2>
R9C2 can only be <7>
R8C6 can only be <7>
R9C6 can only be <5>
R9C7 can only be <3>
R9C3 can only be <8>
R1C2 can only be <2>
R9C8 can only be <2>
R1C7 can only be <5>
R5C8 can only be <4>
R1C4 can only be <9>
R1C3 can only be <7>
R2C4 can only be <2>
R1C8 can only be <3>
R2C6 can only be <8>
R5C7 can only be <2>
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