Oct 07 - Super Hard
Puzzle Copyright © Kevin Stone
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Reasoning
R2C5 is the only square in row 2 that can be <8>
R6C9 is the only square in row 6 that can be <3>
R3C3 is the only square in row 3 that can be <3>
R1C8 is the only square in row 1 that can be <3>
R7C5 is the only square in row 7 that can be <3>
R9C6 is the only square in column 6 that can be <7>
R9C4 is the only square in row 9 that can be <4>
R7C9 is the only square in row 7 that can be <4>
Squares R2C8 and R2C9 in row 2 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 row.
R2C1 - removing <7> from <179> leaving <19>
R2C2 - removing <5> from <159> leaving <19>
R3C1 is the only square in block 1 that can be <7>
R4C1 is the only square in column 1 that can be <4>
R5C5 is the only square in row 5 that can be <4>
R3C5 can only be <5>
R3C4 can only be <9>
R3C9 can only be <6>
R8C5 can only be <6>
R3C7 can only be <1>
R1C4 can only be <2>
R3C6 can only be <4>
R1C6 can only be <1>
R1C2 is the only square in row 1 that can be <4>
R4C4 is the only square in column 4 that can be <6>
R1C7 is the only square in column 7 that can be <9>
R1C3 can only be <5>
Squares R7C4 and R7C6 in row 7 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 row.
R7C1 - removing <8> from <128> leaving <12>
R7C3 - removing <8> from <168> leaving <16>
R7C7 - removing <58> from <2568> leaving <26>
Intersection of column 7 with block 6. The value <7> only appears in one or more of squares R4C7, R5C7 and R6C7 of column 7. These squares are the ones that intersect with block 6. Thus, the other (non-intersecting) squares of block 6 cannot contain this value.
R4C9 - removing <7> from <257> leaving <25>
Squares R2C8, R2C9, R8C8 and R8C9 form a Type-3 Unique Rectangle on <57>. Upon close inspection, it is clear that:
(R8C8 or R8C9)<28> and R8C1<28> form a naked pair on <28> in row 8. No other squares in the row can contain these possibilities
R8C2 - removing <2> from <25> leaving <5>
R9C2 can only be <9>
R2C2 can only be <1>
R2C1 can only be <9>
R5C2 can only be <2>
R6C1 can only be <8>
R6C4 can only be <5>
R8C1 can only be <2>
R4C3 can only be <7>
R5C3 can only be <1>
R6C6 can only be <2>
R7C4 can only be <8>
R6C7 can only be <7>
R4C6 can only be <8>
R6C3 can only be <9>
R7C6 can only be <5>
R8C9 can only be <7>
R7C1 can only be <1>
R8C8 can only be <8>
R2C9 can only be <5>
R2C8 can only be <7>
R4C9 can only be <2>
R4C7 can only be <5>
R7C3 can only be <6>
R7C7 can only be <2>
R9C3 can only be <8>
R5C8 can only be <6>
R9C7 can only be <6>
R5C7 can only be <8>
R9C8 can only be <5>
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