Dec 22 - Super Hard
Puzzle Copyright © Kevin Stone
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Reasoning
R4C1 can only be <4>
R1C3 is the only square in row 1 that can be <6>
R2C5 is the only square in row 2 that can be <2>
R3C8 is the only square in row 3 that can be <2>
R3C9 is the only square in row 3 that can be <3>
R4C4 is the only square in row 4 that can be <2>
R9C3 is the only square in row 9 that can be <3>
R5C6 is the only square in row 5 that can be <3>
R6C1 is the only square in row 6 that can be <3>
R2C3 is the only square in column 3 that can be <9>
Squares R5C2 and R5C3 in row 5 form a simple naked pair. These 2 squares both contain the 2 possibilities <12>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the row.
R5C5 - removing <1> from <1468> leaving <468>
Intersection of row 9 with block 9. The values <89> only appears in one or more of squares R9C7, R9C8 and R9C9 of row 9. These squares are the ones that intersect with block 9. Thus, the other (non-intersecting) squares of block 9 cannot contain these values.
R7C7 - removing <8> from <145678> leaving <14567>
R7C8 - removing <8> from <578> leaving <57>
R7C9 - removing <8> from <1678> leaving <167>
Intersection of column 4 with block 5. The value <6> only appears in one or more of squares R4C4, R5C4 and R6C4 of column 4. These squares are the ones that intersect with block 5. Thus, the other (non-intersecting) squares of block 5 cannot contain this value.
R5C5 - removing <6> from <468> leaving <48>
R6C5 - removing <6> from <169> leaving <19>
Intersection of column 9 with block 9. The value <1> 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.
R7C7 - removing <1> from <14567> leaving <4567>
R8C7 - removing <1> from <14567> leaving <4567>
R9C7 - removing <1> from <14589> leaving <4589>
Intersection of block 2 with row 1. The value <7> only appears in one or more of squares R1C4, R1C5 and R1C6 of block 2. These squares are the ones that intersect with row 1. Thus, the other (non-intersecting) squares of row 1 cannot contain this value.
R1C2 - removing <7> from <157> leaving <15>
R1C7 - removing <7> from <15789> leaving <1589>
R1C8 - removing <7> from <5789> leaving <589>
Squares R9C2<145>, R9C4<45> and R9C6<15> in row 9 form a comprehensive naked triplet. These 3 squares can only contain the 3 possibilities <145>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the row.
R9C7 - removing <45> from <4589> leaving <89>
R9C8 - removing <5> from <589> leaving <89>
Squares R5C2, R5C3, R7C2 and R7C3 form a Type-4 Unique Rectangle on <12>.
R7C2 - removing <1> from <12457> leaving <2457>
R7C3 - removing <1> from <1248> leaving <248>
Squares R9C7, R9C8, R1C7 and R1C8 form a Type-3 Unique Rectangle on <89>. Upon close inspection, it is clear that:
(R1C7 or R1C8)<15> and R1C2<15> form a naked pair on <15> in row 1. No other squares in the row can contain these possibilities
R1C4 - removing <5> from <57> leaving <7>
R1C6 - removing <5> from <578> leaving <78>
(R1C7 or R1C8)<15>, R1C4<57> and R1C2<15> form a naked triplet on <157> in row 1. No other squares in the row can contain these possibilities
R1C6 - removing <7> from <78> leaving <8>
R6C4 can only be <6>
R4C6 can only be <5>
R3C5 can only be <5>
R9C6 can only be <1>
R5C4 can only be <4>
R6C6 can only be <7>
R5C5 can only be <8>
R9C4 can only be <5>
R5C8 can only be <7>
R4C5 can only be <9>
R5C7 can only be <6>
R7C8 can only be <5>
R6C9 can only be <9>
R6C5 can only be <1>
R4C9 can only be <8>
R1C8 can only be <9>
R9C2 can only be <4>
R9C8 can only be <8>
R2C9 can only be <7>
R8C3 can only be <1>
R9C7 can only be <9>
R8C9 can only be <6>
R5C3 can only be <2>
R8C5 can only be <4>
R7C9 can only be <1>
R5C2 can only be <1>
R7C3 can only be <8>
R7C1 can only be <7>
R3C3 can only be <4>
R8C7 can only be <7>
R7C5 can only be <6>
R8C1 can only be <5>
R7C7 can only be <4>
R1C2 can only be <5>
R3C2 can only be <7>
R7C2 can only be <2>
R2C1 can only be <8>
R1C7 can only be <1>
R3C7 can only be <8>
R2C7 can only be <5>
R3C1 can only be <1>
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