The full reasoning can be found below the Sudoku.
Apr 02 - Very Hard
Puzzle Copyright © Kevin Stone
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Reasoning
R2C1 can only be <5>
R2C9 can only be <7>
R8C1 can only be <3>
R1C2 can only be <9>
R2C5 can only be <6>
R8C9 can only be <5>
R7C1 can only be <6>
R8C5 can only be <9>
R1C8 is the only square in row 1 that can be <6>
R6C3 is the only square in row 6 that can be <6>
R9C5 is the only square in row 9 that can be <4>
R9C7 is the only square in row 9 that can be <2>
R7C5 is the only square in row 7 that can be <2>
R9C3 is the only square in row 9 that can be <9>
Squares R1C6 and R7C6 in column 6 form a simple naked pair. These 2 squares both contain the 2 possibilities <13>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the column.
R3C6 - removing <3> from <379> leaving <79>
R5C6 - removing <13> from <13679> leaving <679>
R9C6 - removing <3> from <36> leaving <6>
R5C4 is the only square in row 5 that can be <6>
R5C6 is the only square in row 5 that can be <9>
R3C6 can only be <7>
R3C4 is the only square in row 3 that can be <9>
Squares R5C8 and R6C7 in block 6 form a simple naked pair. These 2 squares both contain the 2 possibilities <37>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the block.
R4C7 - removing <7> from <147> leaving <14>
R5C7 - removing <37> from <13478> leaving <148>
R5C9 - removing <3> from <348> leaving <48>
Intersection of column 5 with block 2. The values <58> only appears in one or more of squares R1C5, R2C5 and R3C5 of column 5. These squares are the ones that intersect with block 2. Thus, the other (non-intersecting) squares of block 2 cannot contain these values.
R1C4 - removing <5> from <135> leaving <13>
Squares R1C4 and R1C6 in row 1 form a simple naked pair. These 2 squares both contain the 2 possibilities <13>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the row.
R1C5 - removing <13> from <1358> leaving <58>
R1C7 - removing <3> from <345> leaving <45>
Squares R1C4 and R1C6 in block 2 form a simple naked pair. These 2 squares both contain the 2 possibilities <13>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the block.
R3C5 - removing <3> from <358> leaving <58>
Squares R1C3 and R1C7 in row 1 and R4C3 and R4C7 in row 4 form a Simple X-Wing pattern on possibility <4>. All other instances of this possibility in columns 3 and 7 can be removed.
R3C3 - removing <4> from <248> leaving <28>
R3C7 - removing <4> from <345> leaving <35>
R5C3 - removing <4> from <2457> leaving <257>
R5C7 - removing <4> from <148> leaving <18>
Squares R5C2 and R9C2 in column 2 and R5C8 and R9C8 in column 8 form a Simple X-Wing pattern on possibility <7>. All other instances of this possibility in rows 5 and 9 can be removed.
R5C3 - removing <7> from <257> leaving <25>
R5C5 - removing <7> from <137> leaving <13>
Squares R1C4, R1C6, R7C4 and R7C6 form a Type-1 Unique Rectangle on <13>.
R7C4 - removing <13> from <135> leaving <5>
R7C3 can only be <7>
R9C4 can only be <3>
R9C8 can only be <7>
R1C4 can only be <1>
R7C6 can only be <1>
R9C2 can only be <5>
R5C8 can only be <3>
R1C6 can only be <3>
R5C5 can only be <1>
R6C7 can only be <7>
R6C5 can only be <3>
R4C3 can only be <4>
R5C2 can only be <7>
R4C7 can only be <1>
R1C3 can only be <8>
R5C1 can only be <2>
R4C5 can only be <7>
R5C7 can only be <8>
R5C3 can only be <5>
R3C1 can only be <4>
R5C9 can only be <4>
R7C7 can only be <3>
R3C9 can only be <3>
R7C9 can only be <8>
R3C7 can only be <5>
R1C5 can only be <5>
R3C3 can only be <2>
R1C7 can only be <4>
R3C5 can only be <8>
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