The full reasoning can be found below the Sudoku.
Sep 06 - Very Hard
Puzzle Copyright © Kevin Stone
Reasoning
R2C3 can only be <3>
R2C7 can only be <6>
R3C2 can only be <7>
R2C4 can only be <5>
R2C6 can only be <8>
R3C8 can only be <3>
R1C1 can only be <2>
R1C9 can only be <7>
R5C9 is the only square in row 5 that can be <6>
R5C3 is the only square in row 5 that can be <9>
R4C8 is the only square in row 4 that can be <9>
R5C7 is the only square in row 5 that can be <8>
R4C3 is the only square in row 4 that can be <8>
R6C2 is the only square in row 6 that can be <6>
R8C6 is the only square in row 8 that can be <6>
R1C6 can only be <3>
R1C4 can only be <9>
R1C5 can only be <6>
R7C5 is the only square in row 7 that can be <9>
R9C4 is the only square in row 9 that can be <3>
Squares R6C3 and R6C8 in row 6 form a simple naked pair. These 2 squares both contain the 2 possibilities <17>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the row.
R6C1 - removing <7> from <3457> leaving <345>
R6C5 - removing <1> from <145> leaving <45>
R6C7 - removing <7> from <247> leaving <24>
R6C9 - removing <1> from <123> leaving <23>
Intersection of row 5 with block 5. The value <1> 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.
R4C5 - removing <1> from <145> leaving <45>
Squares R4C5 and R6C5 in column 5 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 column.
R3C5 - removing <4> from <124> leaving <12>
R9C5 - removing <5> from <125> leaving <12>
Squares R9C5 and R9C9 in row 9 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.
R9C6 - removing <1> from <157> leaving <57>
Squares R4C5 and R6C5 in block 5 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.
R5C4 - removing <4> from <147> leaving <17>
R5C6 - removing <4> from <147> leaving <17>
R5C1 is the only square in row 5 that can be <4>
Squares R7C8 and R8C3 form a remote naked pair. <17> can be removed from any square that is common to their groups.
R8C7 - removing <7> from <27> leaving <2>
R7C2 - removing <1> from <15> leaving <5>
R4C2 can only be <1>
R9C1 can only be <7>
R6C7 can only be <4>
R9C9 can only be <1>
R9C6 can only be <5>
R8C3 can only be <1>
R9C5 can only be <2>
R4C9 can only be <3>
R7C8 can only be <7>
R6C3 can only be <7>
R4C1 can only be <5>
R6C9 can only be <2>
R6C8 can only be <1>
R6C5 can only be <5>
R4C7 can only be <7>
R8C4 can only be <7>
R5C4 can only be <1>
R3C5 can only be <1>
R3C6 can only be <4>
R3C4 can only be <2>
R7C6 can only be <1>
R4C5 can only be <4>
R6C1 can only be <3>
R5C6 can only be <7>
R7C4 can only be <4>
Today's Puzzles
All daily items change at midnight GMT. set time zone