The full reasoning can be found below the Sudoku.
Apr 06 - Super Hard
Puzzle Copyright © Kevin Stone
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Reasoning
R5C5 can only be <3>
R8C8 can only be <8>
R4C8 can only be <1>
R5C3 is the only square in row 5 that can be <1>
Squares R2C6 and R2C8 in row 2 form a simple naked pair. These 2 squares both contain the 2 possibilities <25>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the row.
R2C4 - removing <5> from <4579> leaving <479>
R2C5 - removing <2> from <2479> leaving <479>
Squares R2C2 and R8C2 in column 2 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 column.
R4C2 - removing <79> from <3679> leaving <36>
R5C2 - removing <7> from <267> leaving <26>
R6C2 - removing <9> from <239> leaving <23>
Intersection of column 1 with block 4. The values <89> only appears in one or more of squares R4C1, R5C1 and R6C1 of column 1. These squares are the ones that intersect with block 4. Thus, the other (non-intersecting) squares of block 4 cannot contain these values.
R4C3 - removing <9> from <79> leaving <7>
R6C3 - removing <9> from <459> leaving <45>
Squares R5C1 and R6C3 in block 4 form a simple naked pair. These 2 squares both contain the 2 possibilities <45>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the block.
R6C1 - removing <45> from <4589> leaving <89>
Squares R9C1<47>, R9C5<247> and R9C9<27> in row 9 form a comprehensive naked triplet. These 3 squares can only contain the 3 possibilities <247>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the row.
R9C4 - removing <47> from <1457> leaving <15>
R9C6 - removing <2> from <125> leaving <15>
Squares R3C3<59>, R3C4<359> and R3C7<35> in row 3 form a comprehensive naked triplet. These 3 squares can only contain the 3 possibilities <359>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the row.
R3C5 - removing <9> from <689> leaving <68>
R3C6 - removing <35> from <3568> leaving <68>
Squares R9C4, R9C6, R1C4 and R1C6 form a Type-3 Unique Rectangle on <15>. Upon close inspection, it is clear that:
(R1C4 or R1C6)<237>, R1C9<23> and R1C5<27> form a naked triplet on <237> in row 1. No other squares in the row can contain these possibilities
R1C1 - removing <7> from <57> leaving <5>
R5C1 can only be <4>
R3C3 can only be <9>
R7C3 can only be <4>
R2C2 can only be <7>
R9C1 can only be <7>
R6C3 can only be <5>
R9C9 can only be <2>
R8C2 can only be <9>
R9C5 can only be <4>
R1C9 can only be <3>
R7C7 can only be <7>
R6C9 can only be <9>
R3C7 can only be <5>
R3C4 can only be <3>
R2C8 can only be <2>
R6C1 can only be <8>
R4C9 can only be <6>
R7C4 can only be <9>
R5C7 can only be <2>
R2C5 can only be <9>
R2C4 can only be <4>
R2C6 can only be <5>
R5C8 can only be <5>
R6C8 can only be <4>
R8C4 can only be <7>
R4C2 can only be <3>
R5C9 can only be <7>
R5C2 can only be <6>
R6C7 can only be <3>
R4C1 can only be <9>
R6C2 can only be <2>
R4C7 can only be <8>
R8C5 can only be <6>
R1C4 can only be <1>
R8C6 can only be <3>
R3C5 can only be <8>
R1C6 can only be <2>
R9C4 can only be <5>
R1C5 can only be <7>
R7C6 can only be <8>
R9C6 can only be <1>
R3C6 can only be <6>
R7C5 can only be <2>
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