Feb 10 - Super Hard
Puzzle Copyright © Kevin Stone
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Reasoning
R5C5 can only be <8>
R1C7 is the only square in row 1 that can be <5>
R3C4 is the only square in row 3 that can be <6>
R3C7 is the only square in row 3 that can be <2>
R2C8 can only be <1>
R3C9 can only be <8>
R6C8 is the only square in row 6 that can be <5>
R6C1 is the only square in row 6 that can be <2>
R4C8 is the only square in row 4 that can be <2>
R7C4 is the only square in row 7 that can be <2>
R2C5 is the only square in row 2 that can be <2>
R7C6 is the only square in row 7 that can be <5>
R2C4 is the only square in block 2 that can be <9>
R2C2 can only be <4>
R2C6 can only be <8>
Squares R1C3 and R1C4 in row 1 form a simple naked pair. These 2 squares both contain the 2 possibilities <13>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the row.
R1C6 - removing <13> from <1347> leaving <47>
Squares R5C1 and R5C8 in row 5 form a simple naked pair. These 2 squares both contain the 2 possibilities <79>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the row.
R5C2 - removing <9> from <169> leaving <16>
R5C9 - removing <7> from <167> leaving <16>
Squares R4C2 and R8C2 in column 2 form a simple naked pair. These 2 squares both contain the 2 possibilities <89>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the column.
R6C2 - removing <8> from <168> leaving <16>
Squares R5C2 and R6C2 in block 4 form a simple naked pair. These 2 squares both contain the 2 possibilities <16>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the block.
R6C3 - removing <1> from <148> leaving <48>
Intersection of row 7 with block 9. The value <1> 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 <1> from <149> leaving <49>
Intersection of row 8 with block 8. The values <34> only appears in one or more of squares R8C4, R8C5 and R8C6 of row 8. These squares are the ones that intersect with block 8. Thus, the other (non-intersecting) squares of block 8 cannot contain these values.
R9C5 - removing <4> from <479> leaving <79>
R9C6 - removing <4> from <147> leaving <17>
Squares R1C5, R1C6, R8C5 and R8C6 form a Type-3 Unique Rectangle on <47>. Upon close inspection, it is clear that:
(R8C5 or R8C6)<39>, R8C4<38> and R8C2<89> form a naked triplet on <389> in row 8. No other squares in the row can contain these possibilities
R8C8 - removing <9> from <79> leaving <7>
R5C8 can only be <9>
R5C1 can only be <7>
R4C9 is the only square in row 4 that can be <7>
R7C3 is the only square in row 7 that can be <7>
Squares R5C2, R5C9, R6C2 and R6C9 form a Type-1 Unique Rectangle on <16>.
R6C9 - removing <16> from <146> leaving <4>
R6C3 can only be <8>
R7C9 can only be <1>
R4C7 can only be <8>
R5C9 can only be <6>
R4C2 can only be <9>
R6C7 can only be <1>
R5C2 can only be <1>
R6C2 can only be <6>
R8C2 can only be <8>
R8C4 can only be <3>
R8C6 can only be <4>
R1C4 can only be <1>
R8C5 can only be <9>
R1C6 can only be <7>
R1C3 can only be <3>
R9C4 can only be <8>
R3C6 can only be <3>
R1C5 can only be <4>
R9C6 can only be <1>
R3C1 can only be <9>
R9C5 can only be <7>
R4C3 can only be <4>
R3C3 can only be <1>
R7C1 can only be <4>
R4C1 can only be <3>
R9C3 can only be <9>
R7C7 can only be <9>
R9C7 can only be <4>
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