Jan 29 - Very Hard
Puzzle Copyright © Kevin Stone
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Reasoning
R8C9 can only be <6>
R2C5 is the only square in row 2 that can be <2>
R4C4 is the only square in row 4 that can be <9>
R8C3 is the only square in row 8 that can be <1>
R2C1 is the only square in row 2 that can be <1>
R2C7 is the only square in row 2 that can be <5>
R1C1 is the only square in row 1 that can be <5>
R8C6 is the only square in row 8 that can be <2>
R9C3 is the only square in row 9 that can be <2>
R5C2 is the only square in row 5 that can be <2>
R9C5 is the only square in row 9 that can be <9>
R1C6 is the only square in column 6 that can be <4>
R1C9 is the only square in column 9 that can be <9>
R1C2 can only be <7>
R1C7 can only be <6>
R2C3 can only be <6>
R1C4 can only be <3>
R3C7 can only be <7>
R2C4 can only be <7>
R3C8 can only be <1>
R1C5 can only be <1>
R5C6 is the only square in row 5 that can be <1>
R5C3 is the only square in column 3 that can be <7>
Intersection of row 4 with block 6. The value <5> only appears in one or more of squares R4C7, R4C8 and R4C9 of row 4. These squares are the ones that intersect with block 6. Thus, the other (non-intersecting) squares of block 6 cannot contain this value.
R5C8 - removing <5> from <3456> leaving <346>
Intersection of row 5 with block 6. The value <4> only appears in one or more of squares R5C7, R5C8 and R5C9 of row 5. These squares are the ones that intersect with block 6. Thus, the other (non-intersecting) squares of block 6 cannot contain this value.
R4C8 - removing <4> from <456> leaving <56>
Squares R7C2<489>, R7C3<49> and R7C7<48> in row 7 form a comprehensive naked triplet. These 3 squares can only contain the 3 possibilities <489>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the row.
R7C5 - removing <8> from <568> leaving <56>
R7C8 - removing <4> from <457> leaving <57>
Squares R7C8 and R9C9 in block 9 form a simple naked pair. These 2 squares both contain the 2 possibilities <57>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the block.
R9C8 - removing <57> from <3457> leaving <34>
Squares R6C6 and R6C8 in row 6 and R9C6 and R9C8 in row 9 form a Simple X-Wing pattern on possibility <3>. All other instances of this possibility in columns 6 and 8 can be removed.
R5C8 - removing <3> from <346> leaving <46>
Squares R3C2, R3C3, R7C2 and R7C3 form a Type-1 Unique Rectangle on <49>.
R7C2 - removing <49> from <489> leaving <8>
R7C7 can only be <4>
R6C2 can only be <1>
R9C1 can only be <4>
R7C3 can only be <9>
R5C7 can only be <3>
R9C8 can only be <3>
R4C1 can only be <6>
R9C6 can only be <7>
R8C7 can only be <8>
R4C8 can only be <5>
R6C1 can only be <8>
R4C9 can only be <1>
R7C8 can only be <7>
R4C2 can only be <4>
R6C9 can only be <7>
R6C8 can only be <6>
R9C9 can only be <5>
R3C3 can only be <4>
R7C6 can only be <6>
R8C5 can only be <3>
R9C4 can only be <8>
R3C2 can only be <9>
R6C6 can only be <3>
R5C8 can only be <4>
R7C5 can only be <5>
R3C4 can only be <6>
R3C5 can only be <8>
R5C4 can only be <5>
R5C5 can only be <6>
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