Jul 26 - Very Hard
Puzzle Copyright © Kevin Stone
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Reasoning
R4C8 can only be <1>
R5C1 can only be <2>
R5C5 can only be <5>
R5C6 can only be <1>
R5C9 can only be <7>
R5C4 can only be <6>
R6C8 can only be <5>
R2C8 can only be <2>
R8C8 can only be <6>
R1C8 can only be <7>
R9C8 can only be <4>
R1C1 is the only square in row 1 that can be <4>
R3C3 is the only square in row 3 that can be <2>
R1C5 is the only square in row 1 that can be <2>
R1C9 is the only square in row 1 that can be <8>
R3C7 is the only square in row 3 that can be <6>
R4C6 is the only square in row 4 that can be <2>
R4C5 is the only square in row 4 that can be <4>
R6C4 is the only square in row 6 that can be <7>
R6C2 is the only square in row 6 that can be <9>
R4C2 can only be <3>
R4C4 can only be <9>
R2C1 is the only square in row 2 that can be <9>
R7C9 is the only square in row 7 that can be <2>
R7C3 is the only square in row 7 that can be <9>
R8C2 is the only square in row 8 that can be <2>
R9C9 is the only square in row 9 that can be <9>
R8C6 is the only square in column 6 that can be <5>
Squares R2C4 and R2C6 in row 2 form a simple naked pair. These 2 squares both contain the 2 possibilities <38>. 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 <135> leaving <15>
Squares R3C1 and R7C1 in column 1 form a simple naked pair. These 2 squares both contain the 2 possibilities <35>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the column.
R8C1 - removing <3> from <138> leaving <18>
R9C1 - removing <35> from <1358> leaving <18>
Squares R8C1 and R9C1 in block 7 form a simple naked pair. These 2 squares both contain the 2 possibilities <18>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the block.
R9C2 - removing <1> from <156> leaving <56>
Squares R3C9 and R7C7 form a remote naked pair. <35> can be removed from any square that is common to their groups.
R1C7 - removing <3> from <13> leaving <1>
R8C9 - removing <3> from <13> leaving <1>
R1C2 can only be <6>
R2C9 can only be <5>
R2C2 can only be <1>
R3C9 can only be <3>
R3C1 can only be <5>
R8C1 can only be <8>
R1C3 can only be <3>
R9C2 can only be <5>
R9C3 can only be <6>
R7C1 can only be <3>
R7C7 can only be <5>
R9C7 can only be <3>
R8C4 can only be <3>
R9C1 can only be <1>
R2C4 can only be <8>
R9C5 can only be <8>
R6C5 can only be <3>
R2C6 can only be <3>
R6C6 can only be <8>
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