The full reasoning can be found below the Sudoku.
Apr 02 - Super Hard
Puzzle Copyright © Kevin Stone
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Reasoning
R6C2 can only be <5>
R6C5 can only be <3>
R6C8 can only be <2>
R1C1 is the only square in row 1 that can be <5>
R1C9 is the only square in row 1 that can be <9>
R1C3 is the only square in row 1 that can be <2>
R2C7 is the only square in row 2 that can be <3>
R3C9 is the only square in row 3 that can be <2>
R5C1 is the only square in row 5 that can be <3>
R7C5 is the only square in row 7 that can be <9>
R5C6 is the only square in row 5 that can be <9>
R8C1 is the only square in row 8 that can be <2>
R9C8 is the only square in row 9 that can be <3>
R9C3 is the only square in row 9 that can be <9>
Intersection of row 8 with block 9. The value <8> only appears in one or more of squares R8C7, R8C8 and R8C9 of row 8. 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 <8> from <4568> leaving <456>
R9C9 - removing <8> from <1568> leaving <156>
Squares R2C3 and R8C3 in column 3 and R2C6 and R8C6 in column 6 form a Simple X-Wing pattern on possibility <4>. All other instances of this possibility in rows 2 and 8 can be removed.
R2C4 - removing <4> from <148> leaving <18>
R8C4 - removing <4> from <14> leaving <1>
R8C7 - removing <4> from <468> leaving <68>
R2C4 can only be <8>
R5C4 can only be <4>
R1C5 is the only square in column 5 that can be <1>
Squares R8C9 (XYZ), R8C7 (XZ) and R2C9 (YZ) form an XYZ-Wing pattern on <6>. All squares that are buddies of all three squares cannot be <6>.
R7C9 - removing <6> from <167> leaving <17>
R9C9 - removing <6> from <156> leaving <15>
Intersection of row 7 with block 7. The value <6> only appears in one or more of squares R7C1, R7C2 and R7C3 of row 7. 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 <6> from <168> leaving <18>
R9C2 - removing <6> from <1468> leaving <148>
Squares R2C6 and R8C6 in column 6 and R2C9 and R8C9 in column 9 form a Simple X-Wing pattern on possibility <6>. All other instances of this possibility in rows 2 and 8 can be removed.
R2C1 - removing <6> from <167> leaving <17>
R8C7 - removing <6> from <68> leaving <8>
R5C7 can only be <5>
R9C9 is the only square in row 9 that can be <5>
R5C9 is the only square in column 9 that can be <8>
R5C5 can only be <7>
R4C8 can only be <1>
R4C2 can only be <7>
R5C3 can only be <1>
R4C5 can only be <8>
R2C1 is the only square in row 2 that can be <1>
R9C1 can only be <8>
R9C2 is the only square in row 9 that can be <1>
R7C9 is the only square in row 7 that can be <1>
Squares R1C7 and R3C5 form a remote naked pair. <46> can be removed from any square that is common to their groups.
R3C8 - removing <4> from <478> leaving <78>
Intersection of block 3 with row 1. The value <4> only appears in one or more of squares R1C7, R1C8 and R1C9 of block 3. 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 <4> from <468> leaving <68>
The puzzle can be reduced to a Bivalue Universal Grave (BUG) pattern, by making this reduction:
R3C2=<48>
These are called the BUG possibilities. In a BUG pattern, in each row, column and block, each unsolved possibility appears exactly twice. Such a pattern either has 0 or 2 solutions, so it cannot be part of a valid Sudoku
When a puzzle contains a BUG, and only one square in the puzzle has more than 2 possibilities, the only way to kill the BUG is to remove both of the BUG possibilities from the square, thus solving it
R3C2 - removing <48> from <468> leaving <6>
R3C1 can only be <7>
R3C5 can only be <4>
R1C2 can only be <8>
R7C2 can only be <4>
R9C5 can only be <6>
R2C6 can only be <6>
R7C8 can only be <7>
R8C3 can only be <7>
R7C1 can only be <6>
R3C8 can only be <8>
R8C9 can only be <6>
R2C3 can only be <4>
R8C6 can only be <4>
R2C9 can only be <7>
R9C7 can only be <4>
R1C7 can only be <6>
R1C8 can only be <4>
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