Feb 07 - Super Hard
Puzzle Copyright © Kevin Stone
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Reasoning
R2C9 is the only square in row 2 that can be <4>
R4C6 is the only square in row 4 that can be <1>
R7C6 can only be <9>
R7C4 can only be <5>
R9C5 can only be <1>
R7C5 can only be <7>
R5C8 is the only square in row 5 that can be <8>
R9C9 is the only square in row 9 that can be <8>
Intersection of row 5 with block 4. The value <2> only appears in one or more of squares R5C1, R5C2 and R5C3 of row 5. These squares are the ones that intersect with block 4. Thus, the other (non-intersecting) squares of block 4 cannot contain this value.
R4C1 - removing <2> from <23578> leaving <3578>
R4C2 - removing <2> from <235> leaving <35>
R6C1 - removing <2> from <24578> leaving <4578>
R6C2 - removing <2> from <245> leaving <45>
Squares R4C2<35>, R5C2<234>, R5C3<23> and R6C2<45> in block 4 form a comprehensive naked quad. These 4 squares can only contain the 4 possibilities <2345>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the block.
R4C1 - removing <35> from <3578> leaving <78>
R6C1 - removing <45> from <4578> leaving <78>
R9C1 is the only square in column 1 that can be <4>
Intersection of column 1 with block 1. The value <5> only appears in one or more of squares R1C1, R2C1 and R3C1 of column 1. 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 <5> from <2569> leaving <269>
Squares R3C1 and R3C7 in row 3 and R7C1 and R7C7 in row 7 form a Simple X-Wing pattern on possibility <1>. All other instances of this possibility in columns 1 and 7 can be removed.
R2C1 - removing <1> from <139> leaving <39>
R8C1 - removing <1> from <139> leaving <39>
Squares R2C1 and R8C1 in column 1 form a simple naked pair. These 2 squares both contain the 2 possibilities <39>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the column.
R1C1 - removing <9> from <259> leaving <25>
R3C1 - removing <39> from <1359> leaving <15>
R7C1 - removing <3> from <123> leaving <12>
Squares R3C3 and R3C9 in row 3 and R7C3 and R7C9 in row 7 form a Simple X-Wing pattern on possibility <6>. All other instances of this possibility in columns 3 and 9 can be removed.
R1C9 - removing <6> from <679> leaving <79>
Squares R1C8 (XYZ), R1C9 (XZ) and R9C8 (YZ) form an XYZ-Wing pattern on <9>. All squares that are buddies of all three squares cannot be <9>.
R2C8 - removing <9> from <139> leaving <13>
Intersection of row 2 with block 1. The value <9> only appears in one or more of squares R2C1, R2C2 and R2C3 of row 2. 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 <9> from <269> leaving <26>
Squares R3C3 (XY), R5C3 (XZ) and R1C2 (YZ) form an XY-Wing pattern on <2>. All squares that are buddies of both the XZ and YZ squares cannot be <2>.
R5C2 - removing <2> from <234> leaving <34>
R5C3 is the only square in row 5 that can be <2>
R7C1 is the only square in row 7 that can be <2>
R1C1 can only be <5>
R1C5 can only be <9>
R3C1 can only be <1>
R1C9 can only be <7>
R5C5 can only be <4>
R3C4 can only be <8>
R1C8 can only be <6>
R3C6 can only be <4>
R4C4 can only be <2>
R3C5 can only be <5>
R6C6 can only be <8>
R6C4 can only be <9>
R5C2 can only be <3>
R6C1 can only be <7>
R1C2 can only be <2>
R9C8 can only be <9>
R5C7 can only be <9>
R2C2 can only be <9>
R4C2 can only be <5>
R3C7 can only be <3>
R6C8 can only be <5>
R4C1 can only be <8>
R6C2 can only be <4>
R6C9 can only be <2>
R4C9 can only be <3>
R9C2 can only be <6>
R2C1 can only be <3>
R8C2 can only be <1>
R3C3 can only be <6>
R3C9 can only be <9>
R7C7 can only be <1>
R2C8 can only be <1>
R4C8 can only be <7>
R7C9 can only be <6>
R8C9 can only be <5>
R8C8 can only be <3>
R7C3 can only be <3>
R8C1 can only be <9>
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