Nov 22 - Super Hard
Puzzle Copyright © Kevin Stone
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Reasoning
R5C9 can only be <5>
R1C9 is the only square in row 1 that can be <8>
R5C4 is the only square in row 5 that can be <2>
R6C6 is the only square in row 6 that can be <8>
R9C5 is the only square in row 9 that can be <6>
R5C5 can only be <9>
R3C6 is the only square in column 6 that can be <9>
R2C8 is the only square in column 8 that can be <6>
Squares R6C5 and R6C7 in row 6 form a simple naked pair. These 2 squares both contain the 2 possibilities <14>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the row.
R6C4 - removing <1> from <135> leaving <35>
Squares R7C4 and R7C6 in row 7 form a simple naked pair. These 2 squares both contain the 2 possibilities <13>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the row.
R7C1 - removing <13> from <134579> leaving <4579>
R7C3 - removing <3> from <3579> leaving <579>
R7C7 - removing <13> from <13459> leaving <459>
R7C9 - removing <1> from <1479> leaving <479>
Squares R2C2 and R8C2 in column 2 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.
R1C2 - removing <3> from <345> leaving <45>
R9C2 - removing <23> from <2345> leaving <45>
Squares R4C7 and R6C7 in column 7 form a simple naked pair. These 2 squares both contain the 2 possibilities <14>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the column.
R1C7 - removing <1> from <1359> leaving <359>
R3C7 - removing <1> from <125> leaving <25>
R7C7 - removing <4> from <459> leaving <59>
R9C7 - removing <14> from <123459> leaving <2359>
Intersection of row 2 with block 1. The value <3> 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.
R1C1 - removing <3> from <34579> leaving <4579>
R1C3 - removing <3> from <3579> leaving <579>
Intersection of block 4 with column 3. The value <5> only appears in one or more of squares R4C3, R5C3 and R6C3 of block 4. These squares are the ones that intersect with column 3. Thus, the other (non-intersecting) squares of column 3 cannot contain this value.
R1C3 - removing <5> from <579> leaving <79>
R3C3 - removing <5> from <2567> leaving <267>
R7C3 - removing <5> from <579> leaving <79>
R9C3 - removing <5> from <2359> leaving <239>
Squares R1C3 and R7C3 in column 3 form a simple naked pair. These 2 squares both contain the 2 possibilities <79>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the column.
R3C3 - removing <7> from <267> leaving <26>
R9C3 - removing <9> from <239> leaving <23>
Squares R8C2 and R9C3 in block 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 block.
R8C1 - removing <3> from <137> leaving <17>
R9C1 - removing <3> from <13459> leaving <1459>
Squares R2C2 and R2C9 in row 2 and R8C2 and R8C9 in row 8 form a Simple X-Wing pattern on possibility <2>. All other instances of this possibility in columns 2 and 9 can be removed.
R3C9 - removing <2> from <12> leaving <1>
R9C9 - removing <2> from <1249> leaving <149>
R3C4 can only be <7>
R1C5 can only be <1>
R6C5 can only be <4>
R6C7 can only be <1>
R4C5 can only be <7>
R4C7 can only be <4>
Squares R3C1 and R3C7 in row 3 and R7C1 and R7C7 in row 7 form a Simple X-Wing pattern on possibility <5>. All other instances of this possibility in columns 1 and 7 can be removed.
R1C1 - removing <5> from <4579> leaving <479>
R1C7 - removing <5> from <359> leaving <39>
R9C1 - removing <5> from <1459> leaving <149>
R9C7 - removing <5> from <2359> leaving <239>
Squares R1C7 (XY), R1C8 (XZ) and R7C7 (YZ) form an XY-Wing pattern on <5>. All squares that are buddies of both the XZ and YZ squares cannot be <5>.
R3C7 - removing <5> from <25> leaving <2>
R9C8 - removing <5> from <135> leaving <13>
R3C3 can only be <6>
R2C9 can only be <9>
R2C1 can only be <3>
R9C9 can only be <4>
R1C7 can only be <3>
R3C1 can only be <5>
R4C3 can only be <5>
R4C4 can only be <1>
R6C3 can only be <3>
R4C6 can only be <6>
R7C4 can only be <3>
R5C6 can only be <3>
R5C1 can only be <6>
R7C6 can only be <1>
R6C4 can only be <5>
R9C3 can only be <2>
R8C2 can only be <3>
R9C2 can only be <5>
R7C9 can only be <7>
R1C8 can only be <5>
R9C7 can only be <9>
R1C2 can only be <4>
R2C2 can only be <2>
R7C3 can only be <9>
R8C9 can only be <2>
R8C8 can only be <1>
R8C1 can only be <7>
R9C8 can only be <3>
R9C1 can only be <1>
R7C7 can only be <5>
R7C1 can only be <4>
R1C3 can only be <7>
R1C1 can only be <9>
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