Mar 17 - Super Hard
Puzzle Copyright © Kevin Stone
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Reasoning
R1C3 can only be <7>
R9C8 can only be <8>
R1C2 can only be <9>
R9C7 can only be <5>
R5C8 can only be <7>
R8C7 can only be <2>
R1C7 can only be <1>
R7C9 can only be <9>
R6C1 is the only square in row 6 that can be <7>
R8C2 is the only square in row 8 that can be <7>
R8C1 is the only square in row 8 that can be <9>
R9C4 is the only square in row 9 that can be <1>
R4C9 is the only square in row 4 that can be <1>
R5C5 is the only square in row 5 that can be <1>
R7C1 is the only square in row 7 that can be <1>
R5C1 is the only square in column 1 that can be <5>
R8C5 is the only square in column 5 that can be <3>
R6C9 is the only square in block 6 that can be <2>
R6C4 can only be <5>
Squares R2C3 and R9C3 in column 3 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 column.
R6C3 - removing <3> from <38> leaving <8>
R7C3 - removing <4> from <4568> leaving <568>
R6C6 can only be <3>
R7C2 is the only square in row 7 that can be <8>
Intersection of column 5 with block 2. The value <8> only appears in one or more of squares R1C5, R2C5 and R3C5 of column 5. These squares are the ones that intersect with block 2. Thus, the other (non-intersecting) squares of block 2 cannot contain this value.
R3C6 - removing <8> from <5689> leaving <569>
Squares R8C3, R8C6, R7C3 and R7C6 form a Type-1 Unique Rectangle on <56>.
R7C6 - removing <56> from <2456> leaving <24>
Squares R8C6 (XY), R7C5 (XZ) and R1C6 (YZ) form an XY-Wing pattern on <2>. All squares that are buddies of both the XZ and YZ squares cannot be <2>.
R7C6 - removing <2> from <24> leaving <4>
R2C5 - removing <2> from <28> leaving <8>
R3C5 can only be <5>
R7C5 can only be <2>
R7C4 can only be <6>
R7C3 can only be <5>
R8C6 can only be <5>
R8C3 can only be <6>
Squares R2C3 and R2C7 in row 2 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 row.
R2C9 - removing <3> from <37> leaving <7>
R3C4 is the only square in row 3 that can be <7>
Squares R2C7 and R4C1 form a remote naked pair. <34> can be removed from any square that is common to their groups.
R4C7 - removing <3> from <38> leaving <8>
R4C6 can only be <2>
R5C9 can only be <3>
R5C2 can only be <4>
R3C9 can only be <8>
R4C4 can only be <4>
R1C6 can only be <6>
R5C4 can only be <9>
R9C2 can only be <3>
R4C1 can only be <3>
R5C6 can only be <8>
R2C4 can only be <2>
R9C3 can only be <4>
R2C3 can only be <3>
R1C8 can only be <2>
R3C6 can only be <9>
R2C8 can only be <9>
R2C7 can only be <4>
R3C1 can only be <4>
R3C7 can only be <3>
R3C8 can only be <6>
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