Oct 30 - Very Hard
Puzzle Copyright © Kevin Stone
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Reasoning
R1C9 is the only square in row 1 that can be <6>
R4C6 is the only square in row 4 that can be <6>
R8C4 is the only square in row 8 that can be <1>
R8C6 is the only square in row 8 that can be <3>
R2C4 is the only square in row 2 that can be <3>
R9C5 is the only square in row 9 that can be <6>
R5C5 is the only square in column 5 that can be <3>
R7C3 is the only square in column 3 that can be <3>
R1C6 is the only square in column 6 that can be <5>
R3C7 is the only square in column 7 that can be <3>
Squares R2C2 and R8C2 in column 2 form a simple naked pair. These 2 squares both contain the 2 possibilities <29>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the column.
R6C2 - removing <2> from <258> leaving <58>
Squares R4C2 and R6C2 in block 4 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 block.
R4C1 - removing <58> from <34578> leaving <347>
R6C1 - removing <58> from <23578> leaving <237>
Intersection of row 5 with block 4. The value <2> only appears in one or more of squares R5C1, R5C2 and R5C3 of row 5. These squares are the ones that intersect with block 4. Thus, the other (non-intersecting) squares of block 4 cannot contain this value.
R6C1 - removing <2> from <237> leaving <37>
Intersection of row 7 with block 9. The value <4> only appears in one or more of squares R7C7, R7C8 and R7C9 of row 7. These squares are the ones that intersect with block 9. Thus, the other (non-intersecting) squares of block 9 cannot contain this value.
R9C7 - removing <4> from <1459> leaving <159>
R9C9 - removing <4> from <1249> leaving <129>
Squares R2C2 and R8C2 in column 2 and R2C8 and R8C8 in column 8 form a Simple X-Wing pattern on possibility <2>. All other instances of this possibility in rows 2 and 8 can be removed.
R2C6 - removing <2> from <24> leaving <4>
R1C7 is the only square in row 1 that can be <4>
R5C7 can only be <1>
R7C7 can only be <5>
R9C7 can only be <9>
R8C8 can only be <2>
R8C2 can only be <9>
R2C8 can only be <9>
R7C9 can only be <4>
R9C9 can only be <1>
R2C2 can only be <2>
R6C8 can only be <5>
R3C9 can only be <2>
R6C2 can only be <8>
R4C8 can only be <4>
R5C9 can only be <7>
R5C3 can only be <2>
R4C9 can only be <3>
R6C6 can only be <2>
R4C2 can only be <5>
R6C4 can only be <7>
R9C6 can only be <8>
R7C5 can only be <2>
R4C1 can only be <7>
R6C9 can only be <9>
R5C1 can only be <4>
R9C3 can only be <5>
R6C1 can only be <3>
R4C4 can only be <8>
R7C1 can only be <8>
R9C4 can only be <4>
R9C1 can only be <2>
R3C3 can only be <8>
R3C5 can only be <9>
R1C3 can only be <7>
R3C1 can only be <5>
R1C5 can only be <8>
R1C1 can only be <9>
R1C4 can only be <2>
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