Aug 02 - Super Hard
Puzzle Copyright © Kevin Stone
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Reasoning
R5C8 can only be <6>
R7C5 can only be <7>
R8C5 can only be <2>
R9C9 can only be <9>
R9C1 can only be <4>
R9C4 can only be <5>
R8C3 can only be <3>
R9C6 can only be <8>
R8C7 can only be <4>
R4C3 is the only square in row 4 that can be <6>
R4C9 is the only square in row 4 that can be <8>
R5C3 is the only square in row 5 that can be <4>
R5C2 is the only square in row 5 that can be <7>
R6C7 is the only square in row 6 that can be <2>
R6C4 is the only square in row 6 that can be <7>
R3C7 is the only square in column 7 that can be <6>
Squares R1C1 and R3C2 in block 1 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 block.
R2C3 - removing <1> from <158> leaving <58>
R3C3 - removing <19> from <1589> leaving <58>
Squares R2C3 and R3C3 in column 3 form a simple naked pair. These 2 squares both contain the 2 possibilities <58>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the column.
R6C3 - removing <5> from <159> leaving <19>
Squares R2C5 and R2C7 in row 2 and R5C5 and R5C7 in row 5 form a Simple X-Wing pattern on possibility <1>. All other instances of this possibility in columns 5 and 7 can be removed.
R3C5 - removing <1> from <189> leaving <89>
R4C7 - removing <1> from <139> leaving <39>
Squares R3C5 (XY), R2C5 (XZ) and R3C2 (YZ) form an XY-Wing pattern on <1>. All squares that are buddies of both the XZ and YZ squares cannot be <1>.
R3C4 - removing <1> from <134> leaving <34>
R3C2 is the only square in row 3 that can be <1>
R7C2 can only be <9>
R1C1 can only be <9>
R7C3 can only be <1>
R6C3 can only be <9>
Squares R1C6 (XY), R3C4 (XZ) and R7C6 (YZ) form an XY-Wing pattern on <4>. All squares that are buddies of both the XZ and YZ squares cannot be <4>.
R7C4 - removing <4> from <46> leaving <6>
R3C6 - removing <4> from <349> leaving <39>
R7C6 can only be <4>
R1C6 is the only square in row 1 that can be <6>
R3C4 is the only square in row 3 that can be <4>
Squares R4C4 and R6C9 form a remote naked pair. <13> can be removed from any square that is common to their groups.
R6C6 - removing <3> from <35> leaving <5>
R4C7 - removing <3> from <39> leaving <9>
R5C7 can only be <1>
R5C5 can only be <9>
R2C7 can only be <5>
R6C9 can only be <3>
R6C1 can only be <1>
R4C6 can only be <3>
R1C9 can only be <1>
R1C4 can only be <3>
R2C3 can only be <8>
R7C7 can only be <3>
R3C8 can only be <3>
R3C6 can only be <9>
R7C8 can only be <5>
R4C4 can only be <1>
R3C5 can only be <8>
R4C1 can only be <5>
R2C5 can only be <1>
R3C3 can only be <5>
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