Dec 10 - Very Hard
Puzzle Copyright © Kevin Stone
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Reasoning
R4C8 is the only square in row 4 that can be <7>
R5C5 is the only square in row 5 that can be <3>
R5C3 is the only square in row 5 that can be <5>
R5C1 is the only square in row 5 that can be <4>
R1C1 can only be <2>
R5C4 is the only square in row 5 that can be <7>
R5C9 is the only square in row 5 that can be <8>
R6C5 is the only square in row 6 that can be <6>
R9C5 is the only square in column 5 that can be <5>
R2C6 is the only square in column 6 that can be <6>
Squares R1C5 and R1C8 in row 1 form a simple naked pair. These 2 squares both contain the 2 possibilities <48>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the row.
R1C2 - removing <4> from <467> leaving <67>
R1C9 - removing <4> from <467> leaving <67>
Squares R4C2 and R6C2 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.
R8C2 - removing <9> from <346789> leaving <34678>
R9C2 - removing <9> from <469> leaving <46>
R9C1 is the only square in row 9 that can be <9>
R8C1 can only be <3>
R2C1 can only be <1>
R2C3 can only be <4>
R2C9 can only be <2>
R2C2 is the only square in row 2 that can be <3>
R7C8 is the only square in row 7 that can be <3>
R7C3 is the only square in row 7 that can be <1>
R9C8 is the only square in row 9 that can be <1>
R3C2 is the only square in column 2 that can be <5>
Squares R3C5 and R3C8 in row 3 form a simple naked pair. These 2 squares both contain the 2 possibilities <49>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the row.
R3C7 - removing <9> from <679> leaving <67>
Intersection of column 9 with block 9. The value <4> 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 this value.
R8C8 - removing <4> from <245> leaving <25>
Squares R1C2 and R1C9 in row 1 and R9C2 and R9C9 in row 9 form a Simple X-Wing pattern on possibility <6>. All other instances of this possibility in columns 2 and 9 can be removed.
R8C2 - removing <6> from <4678> leaving <478>
R8C9 - removing <6> from <467> leaving <47>
Squares R3C5 and R3C8 in row 3, R4C2 and R4C5 in row 4 and R6C2 and R6C8 in row 6 form a Swordfish pattern on possibility <9>. All other instances of this possibility in columns 2, 5 and 8 can be removed.
R2C8 - removing <9> from <589> leaving <58>
Squares R1C9 and R8C3 form a remote naked pair. <67> can be removed from any square that is common to their groups.
R8C9 - removing <7> from <47> leaving <4>
R9C9 can only be <6>
R9C2 can only be <4>
R1C9 can only be <7>
R1C2 can only be <6>
R3C7 can only be <6>
R3C3 can only be <7>
R8C3 can only be <6>
Squares R6C8 and R8C6 form a remote naked pair. <29> can be removed from any square that is common to their groups.
R8C8 - removing <2> from <25> leaving <5>
R2C8 can only be <8>
R2C4 can only be <9>
R1C8 can only be <4>
R1C5 can only be <8>
R3C8 can only be <9>
R2C7 can only be <5>
R8C4 can only be <8>
R3C5 can only be <4>
R6C8 can only be <2>
R6C2 can only be <9>
R5C7 can only be <9>
R8C2 can only be <7>
R7C5 can only be <2>
R5C6 can only be <2>
R4C2 can only be <2>
R7C7 can only be <7>
R4C5 can only be <9>
R8C6 can only be <9>
R7C2 can only be <8>
R8C7 can only be <2>
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