Jan 16 - Super Hard
Puzzle Copyright © Kevin Stone
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Reasoning
R4C4 can only be <9>
R6C4 can only be <4>
R5C4 can only be <3>
R4C5 is the only square in row 4 that can be <8>
R5C3 is the only square in row 5 that can be <9>
R6C6 is the only square in row 6 that can be <7>
R8C1 is the only square in row 8 that can be <9>
Squares R7C5 and R8C5 in column 5 form a simple naked pair. These 2 squares both contain the 2 possibilities <35>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the column.
R5C5 - removing <5> from <256> leaving <26>
Squares R1C7<68>, R4C7<156>, R6C7<16> and R9C7<58> in column 7 form a comprehensive naked quad. These 4 squares can only contain the 4 possibilities <1568>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the column.
R2C7 - removing <156> from <135679> leaving <379>
R3C7 - removing <58> from <35789> leaving <379>
R5C7 - removing <156> from <1456> leaving <4>
R7C7 - removing <158> from <123458> leaving <234>
R8C7 - removing <156> from <123456> leaving <234>
Squares R7C7 and R8C7 in column 7 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 column.
R2C7 - removing <3> from <379> leaving <79>
R3C7 - removing <3> from <379> leaving <79>
Squares R7C7 and R8C7 in block 9 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.
R7C9 - removing <3> from <135> leaving <15>
R8C9 - removing <3> from <1356> leaving <156>
Intersection of column 7 with block 6. The value <1> only appears in one or more of squares R4C7, R5C7 and R6C7 of column 7. These squares are the ones that intersect with block 6. Thus, the other (non-intersecting) squares of block 6 cannot contain this value.
R5C8 - removing <1> from <156> leaving <56>
Squares R1C3 and R1C7 in row 1 and R4C3 and R4C7 in row 4 form a Simple X-Wing pattern on possibility <6>. All other instances of this possibility in columns 3 and 7 can be removed.
R2C3 - removing <6> from <34567> leaving <3457>
R6C3 - removing <6> from <126> leaving <12>
R6C7 - removing <6> from <16> leaving <1>
R6C3 can only be <2>
R6C5 can only be <6>
R5C5 can only be <2>
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.
R3C3 - removing <8> from <34578> leaving <3457>
R7C3 - removing <8> from <14578> leaving <1457>
Squares R1C7 (XY), R4C7 (XZ) and R3C8 (YZ) form an XY-Wing pattern on <5>. All squares that are buddies of both the XZ and YZ squares cannot be <5>.
R5C8 - removing <5> from <56> leaving <6>
R5C2 can only be <1>
R4C7 can only be <5>
R4C6 can only be <1>
R9C7 can only be <8>
R5C6 can only be <5>
R8C2 can only be <2>
R4C3 can only be <6>
R8C7 can only be <3>
R8C5 can only be <5>
R7C7 can only be <2>
R9C3 can only be <5>
R1C7 can only be <6>
R1C3 can only be <8>
R7C5 can only be <3>
R7C1 can only be <4>
R3C2 can only be <7>
R3C7 can only be <9>
R2C2 can only be <6>
R7C2 can only be <8>
R3C5 can only be <4>
R2C7 can only be <7>
R2C1 can only be <5>
R8C3 can only be <1>
R8C8 can only be <4>
R8C9 can only be <6>
R7C3 can only be <7>
R2C8 can only be <1>
R3C1 can only be <2>
R2C9 can only be <3>
R7C8 can only be <5>
R2C3 can only be <4>
R3C9 can only be <5>
R3C3 can only be <3>
R2C5 can only be <9>
R3C8 can only be <8>
R7C9 can only be <1>
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