May 17 - Super Hard
Puzzle Copyright © Kevin Stone
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Reasoning
R1C2 can only be <5>
R2C7 is the only square in row 2 that can be <5>
R5C3 is the only square in row 5 that can be <8>
R6C3 is the only square in row 6 that can be <5>
R7C3 is the only square in row 7 that can be <2>
R7C7 is the only square in row 7 that can be <8>
R7C9 is the only square in row 7 that can be <6>
R9C6 is the only square in row 9 that can be <5>
R3C5 is the only square in row 3 that can be <5>
R8C1 is the only square in row 8 that can be <5>
R5C8 is the only square in block 6 that can be <4>
Squares R2C4 and R2C9 in row 2 form a simple naked pair. These 2 squares both contain the 2 possibilities <24>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the row.
R2C3 - removing <4> from <467> leaving <67>
Squares R7C5 and R8C6 in block 8 form a simple naked pair. These 2 squares both contain the 2 possibilities <34>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the block.
R7C4 - removing <34> from <3479> leaving <79>
R9C4 - removing <3> from <379> leaving <79>
Squares R7C4 and R9C4 in column 4 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.
R5C4 - removing <7> from <137> leaving <13>
R6C4 - removing <7> from <1237> leaving <123>
Intersection of row 6 with block 6. The value <7> only appears in one or more of squares R6C7, R6C8 and R6C9 of row 6. These squares are the ones that intersect with block 6. Thus, the other (non-intersecting) squares of block 6 cannot contain this value.
R4C7 - removing <7> from <12367> leaving <1236>
R5C7 - removing <7> from <1367> leaving <136>
Intersection of column 4 with block 2. The value <4> only appears in one or more of squares R1C4, R2C4 and R3C4 of column 4. These squares are the ones that intersect with block 2. Thus, the other (non-intersecting) squares of block 2 cannot contain this value.
R1C6 - removing <4> from <2346> leaving <236>
R3C6 - removing <4> from <346> leaving <36>
Intersection of column 5 with block 5. The value <6> only appears in one or more of squares R4C5, R5C5 and R6C5 of column 5. These squares are the ones that intersect with block 5. Thus, the other (non-intersecting) squares of block 5 cannot contain this value.
R4C6 - removing <6> from <23467> leaving <2347>
R5C6 - removing <6> from <367> leaving <37>
R5C7 is the only square in row 5 that can be <6>
R6C5 is the only square in row 6 that can be <6>
Squares R1C7<23>, R2C9<24> and R3C9<34> in block 3 form a comprehensive naked triplet. These 3 squares can only contain the 3 possibilities <234>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the block.
R3C7 - removing <3> from <379> leaving <79>
R3C8 - removing <3> from <3679> leaving <679>
Squares R1C1 (XY), R7C1 (XZ) and R2C3 (YZ) form an XY-Wing pattern on <7>. All squares that are buddies of both the XZ and YZ squares cannot be <7>.
R9C3 - removing <7> from <137> leaving <13>
R3C1 - removing <7> from <1467> leaving <146>
R9C4 is the only square in row 9 that can be <7>
R7C4 can only be <9>
R9C8 is the only square in row 9 that can be <9>
R3C7 is the only square in row 3 that can be <9>
R8C2 is the only square in row 8 that can be <9>
R6C7 is the only square in column 7 that can be <7>
R6C8 can only be <3>
Intersection of column 2 with block 4. The value <1> only appears in one or more of squares R4C2, R5C2 and R6C2 of column 2. 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 <1> from <167> leaving <67>
R4C3 - removing <1> from <1367> leaving <367>
R3C1 is the only square in column 1 that can be <1>
Intersection of block 1 with column 3. The value <7> only appears in one or more of squares R1C3, R2C3 and R3C3 of block 1. These squares are the ones that intersect with column 3. Thus, the other (non-intersecting) squares of column 3 cannot contain this value.
R4C3 - removing <7> from <367> leaving <36>
Squares R2C4 and R2C9 in row 2 and R6C4 and R6C9 in row 6 form a Simple X-Wing pattern on possibility <2>. All other instances of this possibility in columns 4 and 9 can be removed.
R1C4 - removing <2> from <234> leaving <34>
Squares R2C3, R2C8, R3C3 and R3C8 form a Type-1 Unique Rectangle on <67>.
R3C3 - removing <67> from <467> leaving <4>
R3C9 can only be <3>
R1C1 can only be <6>
R3C6 can only be <6>
R9C9 can only be <1>
R1C7 can only be <2>
R9C3 can only be <3>
R6C9 can only be <2>
R8C7 can only be <3>
R4C1 can only be <7>
R2C3 can only be <7>
R1C6 can only be <3>
R4C7 can only be <1>
R2C9 can only be <4>
R2C8 can only be <6>
R3C8 can only be <7>
R2C4 can only be <2>
R7C1 can only be <4>
R4C2 can only be <3>
R6C4 can only be <1>
R7C5 can only be <3>
R7C2 can only be <7>
R4C5 can only be <4>
R8C6 can only be <4>
R8C3 can only be <1>
R4C3 can only be <6>
R1C4 can only be <4>
R4C6 can only be <2>
R5C6 can only be <7>
R5C2 can only be <1>
R5C4 can only be <3>
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