Dec 15 - Super Hard
Puzzle Copyright © Kevin Stone
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Reasoning
R6C7 can only be <3>
R6C3 can only be <9>
R4C7 can only be <1>
R6C5 can only be <7>
R6C9 can only be <6>
R6C4 can only be <8>
R1C4 is the only square in row 1 that can be <1>
R1C8 is the only square in row 1 that can be <6>
R4C1 is the only square in row 4 that can be <6>
R5C4 is the only square in row 5 that can be <6>
R9C2 is the only square in row 9 that can be <6>
R9C6 is the only square in row 9 that can be <8>
R9C4 is the only square in row 9 that can be <5>
R3C5 is the only square in row 3 that can be <5>
R2C7 is the only square in row 2 that can be <5>
R5C6 is the only square in row 5 that can be <5>
R4C3 is the only square in row 4 that can be <5>
R5C5 is the only square in row 5 that can be <2>
R7C5 can only be <3>
R4C5 can only be <9>
R4C6 can only be <3>
Squares R2C8 and R3C8 in column 8 form a simple naked pair. These 2 squares both contain the 2 possibilities <78>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the column.
R7C8 - removing <7> from <147> leaving <14>
R8C8 - removing <7> from <179> leaving <19>
Squares R2C8 and R3C8 in block 3 form a simple naked pair. These 2 squares both contain the 2 possibilities <78>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the block.
R1C9 - removing <7> from <2347> leaving <234>
R3C9 - removing <7> from <237> leaving <23>
Squares R2C2 and R2C6 in row 2 and R7C2 and R7C6 in row 7 form a Simple X-Wing pattern on possibility <2>. All other instances of this possibility in columns 2 and 6 can be removed.
R1C6 - removing <2> from <279> leaving <79>
R3C2 - removing <2> from <238> leaving <38>
R8C2 - removing <2> from <1239> leaving <139>
Squares R3C2 and R5C2 in column 2 form a simple naked pair. These 2 squares both contain the 2 possibilities <38>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the column.
R2C2 - removing <8> from <289> leaving <29>
R8C2 - removing <3> from <139> leaving <19>
R8C3 is the only square in row 8 that can be <3>
Squares R8C2 and R8C8 in row 8 form a simple naked pair. These 2 squares both contain the 2 possibilities <19>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the row.
R8C9 - removing <9> from <279> leaving <27>
Squares R3C4 and R3C9 in row 3 and R8C4 and R8C9 in row 8 form a Simple X-Wing pattern on possibility <2>. All other instances of this possibility in columns 4 and 9 can be removed.
R1C9 - removing <2> from <234> leaving <34>
R9C9 - removing <2> from <2479> leaving <479>
Squares R1C3 (XY), R2C2 (XZ) and R1C6 (YZ) form an XY-Wing pattern on <9>. All squares that are buddies of both the XZ and YZ squares cannot be <9>.
R1C1 - removing <9> from <379> leaving <37>
R2C6 - removing <9> from <279> leaving <27>
R1C6 is the only square in row 1 that can be <9>
Intersection of row 1 with block 1. The value <7> only appears in one or more of squares R1C1, R1C2 and R1C3 of row 1. These squares are the ones that intersect with block 1. Thus, the other (non-intersecting) squares of block 1 cannot contain this value.
R2C1 - removing <7> from <789> leaving <89>
Squares R7C8 (XY), R7C2 (XZ) and R9C7 (YZ) form an XY-Wing pattern on <2>. All squares that are buddies of both the XZ and YZ squares cannot be <2>.
R9C3 - removing <2> from <27> leaving <7>
R1C3 can only be <2>
R7C1 can only be <4>
R1C7 can only be <4>
R2C2 can only be <9>
R1C9 can only be <3>
R9C7 can only be <2>
R1C1 can only be <7>
R3C9 can only be <2>
R2C1 can only be <8>
R8C2 can only be <1>
R3C4 can only be <7>
R8C9 can only be <7>
R7C8 can only be <1>
R9C1 can only be <9>
R7C2 can only be <2>
R8C8 can only be <9>
R5C8 can only be <4>
R9C9 can only be <4>
R8C4 can only be <2>
R5C9 can only be <9>
R2C8 can only be <7>
R5C1 can only be <3>
R3C2 can only be <3>
R2C6 can only be <2>
R3C8 can only be <8>
R5C2 can only be <8>
R7C6 can only be <7>
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