Feb 15 - Super Hard
Puzzle Copyright © Kevin Stone
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Reasoning
R8C6 can only be <3>
R1C2 is the only square in row 1 that can be <7>
R3C8 is the only square in row 3 that can be <6>
R4C4 is the only square in row 4 that can be <9>
R5C5 is the only square in row 5 that can be <3>
R6C6 is the only square in row 6 that can be <7>
Squares R4C2 and R4C6 in row 4 form a simple naked pair. These 2 squares both contain the 2 possibilities <46>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the row.
R4C8 - removing <4> from <248> leaving <28>
Intersection of row 1 with block 3. The value <2> only appears in one or more of squares R1C7, R1C8 and R1C9 of row 1. These squares are the ones that intersect with block 3. Thus, the other (non-intersecting) squares of block 3 cannot contain this value.
R2C7 - removing <2> from <12489> leaving <1489>
R2C8 - removing <2> from <12458> leaving <1458>
R2C9 - removing <2> from <2489> leaving <489>
R3C9 - removing <2> from <249> leaving <49>
R8C9 is the only square in column 9 that can be <2>
R8C7 is the only square in row 8 that can be <9>
Intersection of block 6 with column 8. The value <8> only appears in one or more of squares R4C8, R5C8 and R6C8 of block 6. These squares are the ones that intersect with column 8. Thus, the other (non-intersecting) squares of column 8 cannot contain this value.
R1C8 - removing <8> from <258> leaving <25>
R2C8 - removing <8> from <1458> leaving <145>
R7C8 - removing <8> from <13478> leaving <1347>
R8C8 - removing <8> from <178> leaving <17>
R9C8 - removing <8> from <1348> leaving <134>
Squares R1C3<58>, R2C1<458> and R3C1<45> in block 1 form a comprehensive naked triplet. These 3 squares can only contain the 3 possibilities <458>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the block.
R2C2 - removing <45> from <23459> leaving <239>
R2C3 - removing <458> from <3458> leaving <3>
R3C2 - removing <45> from <2459> leaving <29>
Intersection of block 1 with column 1. The value <4> only appears in one or more of squares R1C1, R2C1 and R3C1 of block 1. These squares are the ones that intersect with column 1. Thus, the other (non-intersecting) squares of column 1 cannot contain this value.
R7C1 - removing <4> from <478> leaving <78>
Squares R1C3 and R1C7 in row 1 and R9C3 and R9C7 in row 9 form a Simple X-Wing pattern on possibility <8>. All other instances of this possibility in columns 3 and 7 can be removed.
R2C7 - removing <8> from <148> leaving <14>
R8C3 - removing <8> from <568> leaving <56>
Squares R5C4 (XY), R5C7 (XZ) and R4C6 (YZ) form an XY-Wing pattern on <4>. All squares that are buddies of both the XZ and YZ squares cannot be <4>.
R5C6 - removing <4> from <456> leaving <56>
R4C6 is the only square in column 6 that can be <4>
R4C2 can only be <6>
R8C3 is the only square in row 8 that can be <6>
Squares R3C1 and R3C5 in row 3, R6C2 and R6C5 in row 6 and R8C1 and R8C2 in row 8 form a Swordfish pattern on possibility <5>. All other instances of this possibility in columns 1, 2 and 5 can be removed.
R2C1 - removing <5> from <458> leaving <48>
Squares R2C9 (XYZ), R2C1 (XZ) and R3C9 (YZ) form an XYZ-Wing pattern on <4>. All squares that are buddies of all three squares cannot be <4>.
R2C7 - removing <4> from <14> leaving <1>
R2C8 - removing <4> from <145> leaving <15>
R2C8 can only be <5>
R2C6 can only be <6>
R1C8 can only be <2>
R1C7 can only be <8>
R4C8 can only be <8>
R2C4 can only be <2>
R5C6 can only be <5>
R4C5 can only be <2>
R6C8 can only be <4>
R5C3 can only be <4>
R6C2 can only be <5>
R5C7 can only be <2>
R1C3 can only be <5>
R9C7 can only be <4>
R2C2 can only be <9>
R5C4 can only be <6>
R3C5 can only be <5>
R3C1 can only be <4>
R9C3 can only be <8>
R8C2 can only be <1>
R8C4 can only be <8>
R8C8 can only be <7>
R6C4 can only be <1>
R7C5 can only be <1>
R8C1 can only be <5>
R7C1 can only be <7>
R9C2 can only be <3>
R7C9 can only be <8>
R2C9 can only be <4>
R3C2 can only be <2>
R2C1 can only be <8>
R3C9 can only be <9>
R6C5 can only be <8>
R7C8 can only be <3>
R7C2 can only be <4>
R9C8 can only be <1>
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