Dec 13 - Super Hard
Puzzle Copyright © Kevin Stone
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Reasoning
R2C7 can only be <5>
R3C2 can only be <5>
R7C4 can only be <4>
R3C8 can only be <9>
R1C8 can only be <2>
R3C4 can only be <8>
R1C9 can only be <6>
R3C6 can only be <7>
R3C5 can only be <4>
R1C1 is the only square in row 1 that can be <7>
R5C3 is the only square in row 5 that can be <7>
R7C5 is the only square in row 7 that can be <7>
R9C8 is the only square in row 9 that can be <4>
R9C4 is the only square in row 9 that can be <6>
R8C3 is the only square in column 3 that can be <8>
Squares R4C3 and R4C8 in row 4 form a simple naked pair. These 2 squares both contain the 2 possibilities <15>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the row.
R4C2 - removing <1> from <169> leaving <69>
R4C5 - removing <5> from <259> leaving <29>
Squares R7C6 and R8C5 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.
R9C5 - removing <23> from <2358> leaving <58>
R9C6 - removing <23> from <2358> leaving <58>
Squares R6C5 and R9C5 in column 5 form a simple naked pair. These 2 squares both contain the 2 possibilities <58>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the column.
R1C5 - removing <5> from <1359> leaving <139>
Intersection of row 9 with block 7. The value <3> only appears in one or more of squares R9C1, R9C2 and R9C3 of row 9. These squares are the ones that intersect with block 7. Thus, the other (non-intersecting) squares of block 7 cannot contain this value.
R7C2 - removing <3> from <123> leaving <12>
Squares R4C3<15>, R5C1<13> and R6C3<35> in block 4 form a comprehensive naked triplet. These 3 squares can only contain the 3 possibilities <135>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the block.
R5C2 - removing <13> from <1349> leaving <49>
R6C2 - removing <3> from <346> leaving <46>
Squares R6C3<35>, R6C5<58> and R6C8<358> in row 6 form a comprehensive naked triplet. These 3 squares can only contain the 3 possibilities <358>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the row.
R6C7 - removing <3> from <346> leaving <46>
Squares R5C1 and R9C1 in column 1 and R5C9 and R9C9 in column 9 form a Simple X-Wing pattern on possibility <1>. All other instances of this possibility in rows 5 and 9 can be removed.
R9C2 - removing <1> from <123> leaving <23>
R5C8 - removing <1> from <1358> leaving <358>
Squares R4C5 and R4C7 in row 4 and R8C5 and R8C7 in row 8 form a Simple X-Wing pattern on possibility <2>. All other instances of this possibility in columns 5 and 7 can be removed.
R5C7 - removing <2> from <234> leaving <34>
Squares R7C2 (XY), R1C2 (XZ) and R7C6 (YZ) form an XY-Wing pattern on <3>. All squares that are buddies of both the XZ and YZ squares cannot be <3>.
R1C6 - removing <3> from <35> leaving <5>
R1C4 can only be <9>
R9C6 can only be <8>
R9C5 can only be <5>
R5C6 can only be <2>
R5C4 can only be <5>
R6C5 can only be <8>
R5C9 can only be <1>
R7C6 can only be <3>
R4C5 can only be <9>
R5C1 can only be <3>
R9C9 can only be <2>
R4C8 can only be <5>
R7C8 can only be <1>
R8C5 can only be <2>
R7C2 can only be <2>
R8C7 can only be <3>
R5C7 can only be <4>
R9C2 can only be <3>
R4C2 can only be <6>
R4C3 can only be <1>
R6C8 can only be <3>
R5C8 can only be <8>
R9C1 can only be <1>
R6C3 can only be <5>
R5C2 can only be <9>
R6C7 can only be <6>
R6C2 can only be <4>
R4C7 can only be <2>
R1C2 can only be <1>
R1C5 can only be <3>
R2C3 can only be <3>
R2C5 can only be <1>
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