Dec 07 - Super Hard
Puzzle Copyright © Kevin Stone
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Reasoning
R2C8 can only be <7>
R7C5 can only be <2>
R3C5 can only be <4>
R9C6 can only be <6>
R9C4 can only be <8>
R6C6 can only be <9>
R4C5 can only be <3>
R6C5 can only be <8>
R1C4 can only be <2>
R5C5 can only be <7>
R5C6 can only be <5>
R5C7 can only be <6>
R4C6 can only be <2>
R5C4 can only be <4>
R6C9 can only be <4>
R6C1 can only be <1>
R4C9 can only be <5>
R1C6 can only be <7>
R5C3 can only be <3>
R4C4 can only be <1>
R6C4 can only be <6>
R4C1 can only be <4>
R1C9 is the only square in row 1 that can be <8>
R2C1 is the only square in row 2 that can be <9>
R8C9 is the only square in row 8 that can be <9>
R9C3 is the only square in row 9 that can be <9>
R1C3 is the only square in column 3 that can be <4>
Intersection of row 8 with block 7. The value <2> only appears in one or more of squares R8C1, R8C2 and R8C3 of row 8. These squares are the ones that intersect with block 7. Thus, the other (non-intersecting) squares of block 7 cannot contain this value.
R9C1 - removing <2> from <237> leaving <37>
R9C2 - removing <2> from <1234> leaving <134>
Squares R3C3 and R3C7 in row 3 and R7C3 and R7C7 in row 7 form a Simple X-Wing pattern on possibility <1>. All other instances of this possibility in columns 3 and 7 can be removed.
R1C7 - removing <1> from <135> leaving <35>
R9C7 - removing <1> from <123> leaving <23>
Squares R9C1<37>, R9C7<23> and R9C9<237> in row 9 form a comprehensive naked triplet. These 3 squares can only contain the 3 possibilities <237>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the row.
R9C2 - removing <3> from <134> leaving <14>
Intersection of column 2 with block 1. The value <3> only appears in one or more of squares R1C2, R2C2 and R3C2 of column 2. These squares are the ones that intersect with block 1. Thus, the other (non-intersecting) squares of block 1 cannot contain this value.
R1C1 - removing <3> from <356> leaving <56>
Squares R1C1<56>, R3C1<256> and R8C1<26> in column 1 form a comprehensive naked triplet. These 3 squares can only contain the 3 possibilities <256>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the column.
R7C1 - removing <6> from <367> leaving <37>
Squares R1C1 and R1C8 in row 1 and R8C1 and R8C8 in row 8 form a Simple X-Wing pattern on possibility <6>. All other instances of this possibility in columns 1 and 8 can be removed.
R3C1 - removing <6> from <256> leaving <25>
Squares R7C1, R9C1, R7C9 and R9C9 form a Type-3 Unique Rectangle on <37>. Upon close inspection, it is clear that:
(R7C9 or R9C9)<26> and R3C9<26> form a naked pair on <26> in column 9. No other squares in the column can contain these possibilities
R2C9 - removing <2> from <23> leaving <3>
R2C2 can only be <2>
R1C7 can only be <5>
R1C1 can only be <6>
R8C2 can only be <4>
R3C1 can only be <5>
R8C8 can only be <6>
R9C2 can only be <1>
R8C1 can only be <2>
R1C8 can only be <1>
R7C9 can only be <7>
R9C8 can only be <4>
R1C2 can only be <3>
R7C3 can only be <6>
R3C3 can only be <1>
R3C7 can only be <2>
R3C9 can only be <6>
R9C7 can only be <3>
R7C1 can only be <3>
R9C9 can only be <2>
R9C1 can only be <7>
R7C7 can only be <1>
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