Jun 02 - Super Hard

Puzzle Copyright © Kevin Stone

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## Reasoning

R1C1 can only be <8>

R4C2 can only be <6>

R6C8 can only be <5>

R4C8 can only be <3>

R4C5 can only be <4>

R6C5 can only be <8>

R5C6 can only be <5>

R5C4 can only be <3>

R8C6 can only be <6>

R6C2 can only be <2>

R2C6 can only be <4>

R5C5 can only be <9>

R8C4 can only be <5>

R2C4 can only be <7>

R3C5 is the only square in row 3 that can be <2>

R1C3 is the only square in row 1 that can be <2>

R5C7 is the only square in row 5 that can be <2>

R5C2 is the only square in row 5 that can be <8>

Squares R3C2 and R3C9 in row 3 and R7C2 and R7C9 in row 7 form a Simple X-Wing pattern on possibility <5>. All other instances of this possibility in columns 2 and 9 can be removed.

R1C9 - removing <5> from <356> leaving <36>

R2C2 - removing <5> from <159> leaving <19>

R9C9 - removing <5> from <569> leaving <69>

Squares R2C2 and R8C2 in column 2 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.

R3C2 - removing <19> from <1579> leaving <57>

Intersection of row 3 with block 3. The value <1> only appears in one or more of squares R3C7, R3C8 and R3C9 of row 3. These squares are the ones that intersect with block 3. Thus, the other (non-intersecting) squares of block 3 cannot contain this value.

R2C8 - removing <1> from <1689> leaving <689>

Squares R2C2 and R2C8 in row 2 and R8C2 and R8C8 in row 8 form a Simple X-Wing pattern on possibility <9>. All other instances of this possibility in columns 2 and 8 can be removed.

R3C8 - removing <9> from <19> leaving <1>

R5C8 can only be <6>

R5C9 can only be <1>

R7C8 can only be <4>

R8C3 is the only square in row 8 that can be <4>

R5C3 can only be <7>

R5C1 can only be <4>

Squares R9C3 (XY), R9C5 (XZ) and R7C2 (YZ) form an XY-Wing pattern on <7>. All squares that are buddies of both the XZ and YZ squares cannot be <7>.

R7C5 - removing <7> from <37> leaving <3>

R9C1 - removing <7> from <679> leaving <69>

R8C5 can only be <1>

R8C2 can only be <9>

R9C5 can only be <7>

R8C8 can only be <8>

R2C2 can only be <1>

R9C1 can only be <6>

R8C7 can only be <3>

R2C8 can only be <9>

R9C7 can only be <5>

R9C9 can only be <9>

R7C1 can only be <7>

R9C3 can only be <1>

R7C9 can only be <6>

R3C9 can only be <5>

R2C3 can only be <5>

R2C5 can only be <6>

R3C2 can only be <7>

R2C7 can only be <8>

R1C5 can only be <5>

R3C1 can only be <9>

R7C2 can only be <5>

R1C9 can only be <3>

R1C7 can only be <6>

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