Aug 14 - Very Hard
Puzzle Copyright © Kevin Stone
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Reasoning
R2C3 can only be <1>
R2C7 can only be <4>
R2C9 can only be <2>
R2C1 can only be <9>
R4C2 is the only square in row 4 that can be <2>
R4C6 is the only square in row 4 that can be <9>
R6C3 is the only square in row 6 that can be <8>
R8C1 is the only square in row 8 that can be <8>
R9C2 is the only square in row 9 that can be <9>
R5C1 is the only square in column 1 that can be <6>
R7C2 is the only square in column 2 that can be <4>
R6C2 is the only square in column 2 that can be <1>
R6C7 can only be <3>
R6C6 can only be <5>
R4C7 can only be <1>
R8C7 can only be <7>
R9C6 is the only square in row 9 that can be <7>
Squares R1C9 and R3C9 in column 9 form a simple naked pair. These 2 squares both contain the 2 possibilities <17>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the column.
R5C9 - removing <7> from <457> leaving <45>
R7C9 - removing <1> from <1356> leaving <356>
R9C9 - removing <1> from <13456> leaving <3456>
R5C8 is the only square in row 5 that can be <7>
Squares R1C9 and R3C9 in block 3 form a simple naked pair. These 2 squares both contain the 2 possibilities <17>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the block.
R1C8 - removing <1> from <189> leaving <89>
R3C8 - removing <1> from <189> leaving <89>
Intersection of column 5 with block 8. The value <6> only appears in one or more of squares R7C5, R8C5 and R9C5 of column 5. These squares are the ones that intersect with block 8. Thus, the other (non-intersecting) squares of block 8 cannot contain this value.
R7C4 - removing <6> from <2356> leaving <235>
R9C4 - removing <6> from <356> leaving <35>
Intersection of column 9 with block 9. The values <36> only appears in one or more of squares R7C9, R8C9 and R9C9 of column 9. These squares are the ones that intersect with block 9. Thus, the other (non-intersecting) squares of block 9 cannot contain these values.
R7C8 - removing <6> from <156> leaving <15>
R9C8 - removing <6> from <1456> leaving <145>
Squares R5C2 and R8C9 form a remote naked pair. <35> can be removed from any square that is common to their groups.
R5C9 - removing <5> from <45> leaving <4>
R5C5 can only be <3>
R6C8 can only be <6>
R6C4 can only be <4>
R4C8 can only be <5>
R4C3 can only be <3>
R7C8 can only be <1>
R5C2 can only be <5>
R9C5 can only be <6>
R4C4 can only be <6>
R9C8 can only be <4>
R7C5 can only be <8>
R8C3 can only be <5>
R3C5 can only be <9>
R8C9 can only be <3>
R7C1 can only be <3>
R9C9 can only be <5>
R9C4 can only be <3>
R7C9 can only be <6>
R3C8 can only be <8>
R1C5 can only be <4>
R1C8 can only be <9>
R7C6 can only be <2>
R1C1 can only be <2>
R9C1 can only be <1>
R7C4 can only be <5>
R3C6 can only be <3>
R1C4 can only be <1>
R3C1 can only be <5>
R1C9 can only be <7>
R3C4 can only be <2>
R1C2 can only be <3>
R3C9 can only be <1>
R3C2 can only be <7>
R1C6 can only be <8>
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