The full reasoning can be found below the Sudoku.
Apr 23 - Very Hard
Puzzle Copyright © Kevin Stone
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Reasoning
R3C1 is the only square in row 3 that can be <6>
R9C5 is the only square in row 9 that can be <1>
R5C1 is the only square in column 1 that can be <5>
R9C1 is the only square in column 1 that can be <7>
R2C3 is the only square in column 3 that can be <1>
Squares R1C1 and R2C1 in block 1 form a simple naked pair. These 2 squares both contain the 2 possibilities <23>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the block.
R1C2 - removing <23> from <2349> leaving <49>
R2C2 - removing <23> from <2349> leaving <49>
Squares R1C2 and R1C7 in row 1 form a simple naked pair. These 2 squares both contain the 2 possibilities <49>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the row.
R1C5 - removing <9> from <279> leaving <27>
R1C9 - removing <4> from <14> leaving <1>
R3C6 is the only square in row 3 that can be <1>
R5C8 is the only square in row 5 that can be <1>
Squares R1C2 and R2C2 in column 2 form a simple naked pair. These 2 squares both contain the 2 possibilities <49>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the column.
R7C2 - removing <4> from <468> leaving <68>
R8C2 - removing <4> from <248> leaving <28>
Intersection of row 5 with block 5. The value <7> only appears in one or more of squares R5C4, R5C5 and R5C6 of row 5. These squares are the ones that intersect with block 5. Thus, the other (non-intersecting) squares of block 5 cannot contain this value.
R4C4 - removing <7> from <257> leaving <25>
R4C5 - removing <7> from <25678> leaving <2568>
R6C5 - removing <7> from <257> leaving <25>
R6C6 - removing <7> from <23457> leaving <2345>
Squares R4C4 and R6C5 in block 5 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 block.
R4C5 - removing <25> from <2568> leaving <68>
R6C6 - removing <25> from <2345> leaving <34>
Intersection of row 7 with block 8. The value <7> only appears in one or more of squares R7C4, R7C5 and R7C6 of row 7. These squares are the ones that intersect with block 8. Thus, the other (non-intersecting) squares of block 8 cannot contain this value.
R8C4 - removing <7> from <24579> leaving <2459>
R8C5 - removing <7> from <2579> leaving <259>
Intersection of column 6 with block 2. The value <2> only appears in one or more of squares R1C6, R2C6 and R3C6 of column 6. These squares are the ones that intersect with block 2. Thus, the other (non-intersecting) squares of block 2 cannot contain this value.
R1C5 - removing <2> from <27> leaving <7>
R2C5 - removing <2> from <259> leaving <59>
Intersection of column 9 with block 9. The values <56> 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 these values.
R8C7 - removing <5> from <45789> leaving <4789>
Squares R4C3 and R4C4 in row 4 and R9C3 and R9C4 in row 9 form a Simple X-Wing pattern on possibility <2>. All other instances of this possibility in columns 3 and 4 can be removed.
R6C3 - removing <2> from <27> leaving <7>
R8C4 - removing <2> from <2459> leaving <459>
Squares R1C1, R1C6, R2C1 and R2C6 form a Type-1 Unique Rectangle on <23>.
R2C6 - removing <23> from <235> leaving <5>
R2C5 can only be <9>
R2C2 can only be <4>
R3C4 can only be <3>
R1C6 can only be <2>
R1C1 can only be <3>
R2C8 can only be <3>
R1C2 can only be <9>
R2C1 can only be <2>
R1C7 can only be <4>
R6C7 can only be <5>
R6C5 can only be <2>
R6C2 can only be <3>
R8C5 can only be <5>
R4C4 can only be <5>
R6C6 can only be <4>
R5C2 can only be <6>
R7C6 can only be <7>
R5C4 can only be <7>
R7C4 can only be <4>
R5C6 can only be <3>
R5C5 can only be <8>
R7C2 can only be <8>
R4C3 can only be <2>
R5C9 can only be <4>
R4C5 can only be <6>
R8C9 can only be <8>
R9C9 can only be <6>
R8C2 can only be <2>
R7C3 can only be <6>
R8C4 can only be <9>
R9C4 can only be <2>
R8C7 can only be <7>
R9C3 can only be <4>
R7C9 can only be <5>
R8C8 can only be <4>
R4C7 can only be <8>
R9C8 can only be <9>
R3C8 can only be <8>
R3C7 can only be <9>
R4C8 can only be <7>
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