May 15 - Super Hard
Puzzle Copyright © Kevin Stone
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Reasoning
R2C9 can only be <1>
R5C9 can only be <3>
R1C5 is the only square in row 1 that can be <3>
R4C5 is the only square in row 4 that can be <5>
R4C4 is the only square in row 4 that can be <6>
R8C1 is the only square in row 8 that can be <8>
R9C9 is the only square in row 9 that can be <2>
R8C3 is the only square in row 8 that can be <2>
R7C2 is the only square in column 2 that can be <3>
Squares R6C4 and R7C4 in column 4 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 column.
R5C4 - removing <19> from <1249> leaving <24>
Intersection of block 4 with row 5. The value <1> only appears in one or more of squares R5C1, R5C2 and R5C3 of block 4. These squares are the ones that intersect with row 5. Thus, the other (non-intersecting) squares of row 5 cannot contain this value.
R5C6 - removing <1> from <1278> leaving <278>
Squares R1C2 and R1C8 in row 1 and R9C2 and R9C8 in row 9 form a Simple X-Wing pattern on possibility <4>. All other instances of this possibility in columns 2 and 8 can be removed.
R3C2 - removing <4> from <457> leaving <57>
R3C8 - removing <4> from <4678> leaving <678>
R7C8 - removing <4> from <4679> leaving <679>
Squares R3C3 and R3C8 in row 3 and R7C3 and R7C8 in row 7 form a Simple X-Wing pattern on possibility <6>. All other instances of this possibility in columns 3 and 8 can be removed.
R1C8 - removing <6> from <46> leaving <4>
R9C8 - removing <6> from <4679> leaving <479>
R9C2 is the only square in row 9 that can be <4>
R7C7 is the only square in row 7 that can be <4>
Intersection of column 7 with block 6. The values <19> 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 these values.
R5C8 - removing <9> from <89> leaving <8>
Squares R6C4 and R6C7 in row 6 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.
R6C3 - removing <9> from <379> leaving <37>
R6C5 - removing <9> from <789> leaving <78>
R6C6 - removing <1> from <1378> leaving <378>
Squares R3C8 (XY), R1C9 (XZ) and R3C2 (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 <578> leaving <78>
R1C2 - removing <5> from <15> leaving <1>
R1C1 can only be <6>
R5C2 can only be <7>
R5C6 can only be <2>
R3C2 can only be <5>
R6C3 can only be <3>
R5C4 can only be <4>
R3C6 can only be <8>
R4C3 can only be <9>
R1C9 can only be <5>
R9C1 can only be <7>
R8C9 can only be <6>
R3C7 can only be <7>
R6C6 can only be <7>
R2C5 can only be <4>
R3C3 can only be <4>
R3C8 can only be <6>
R2C7 can only be <8>
R8C7 can only be <5>
R4C7 can only be <1>
R5C1 can only be <1>
R4C6 can only be <3>
R6C7 can only be <9>
R5C5 can only be <9>
R3C4 can only be <2>
R6C4 can only be <1>
R7C4 can only be <9>
R6C5 can only be <8>
R7C6 can only be <1>
R7C8 can only be <7>
R7C3 can only be <6>
R9C8 can only be <9>
R8C5 can only be <7>
R9C5 can only be <6>
R2C1 can only be <9>
R2C3 can only be <7>
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