Jun 18 - Super Hard
Puzzle Copyright © Kevin Stone
Share link – www.brainbashers.com
Reasoning
R4C4 can only be <9>
R4C6 can only be <7>
R5C7 can only be <2>
R6C4 can only be <3>
R6C6 can only be <5>
R4C5 can only be <2>
R5C6 can only be <8>
R5C8 can only be <7>
R6C5 can only be <1>
R5C4 can only be <4>
R5C5 can only be <6>
R7C3 is the only square in row 7 that can be <7>
R3C3 can only be <3>
R3C5 can only be <7>
R5C3 can only be <9>
R2C5 can only be <3>
R5C2 can only be <3>
R1C8 is the only square in row 1 that can be <3>
R1C2 is the only square in row 1 that can be <5>
R2C3 can only be <6>
R8C3 can only be <5>
R2C8 is the only square in row 2 that can be <5>
R8C7 is the only square in row 8 that can be <3>
R8C9 is the only square in row 8 that can be <4>
Squares R7C5 and R7C7 in row 7 form a simple naked pair. These 2 squares both contain the 2 possibilities <89>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the row.
R7C2 - removing <9> from <269> leaving <26>
R7C8 - removing <8> from <268> leaving <26>
Squares R8C1 and R8C5 in row 8 form a simple naked pair. These 2 squares both contain the 2 possibilities <89>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the row.
R8C2 - removing <9> from <169> leaving <16>
R8C8 - removing <8> from <168> leaving <16>
Squares R3C2 and R3C8 in row 3 and R7C2 and R7C8 in row 7 form a Simple X-Wing pattern on possibility <2>. All other instances of this possibility in columns 2 and 8 can be removed.
R2C2 - removing <2> from <249> leaving <49>
R9C2 - removing <2> from <129> leaving <19>
R9C8 - removing <2> from <128> leaving <18>
Squares R2C2 and R2C7 in row 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 row.
R2C1 - removing <9> from <279> leaving <27>
R2C9 - removing <9> from <279> leaving <27>
The puzzle can be reduced to a Bivalue Universal Grave (BUG) pattern, by making this reduction:
R9C1=<28>
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
R9C1 - removing <28> from <289> leaving <9>
R9C2 can only be <1>
R9C9 can only be <2>
R1C1 can only be <7>
R8C1 can only be <8>
R9C8 can only be <8>
R8C2 can only be <6>
R3C8 can only be <2>
R7C7 can only be <9>
R2C9 can only be <7>
R7C8 can only be <6>
R1C9 can only be <9>
R2C1 can only be <2>
R2C7 can only be <4>
R3C2 can only be <4>
R2C2 can only be <9>
R3C7 can only be <8>
R7C5 can only be <8>
R7C2 can only be <2>
R8C8 can only be <1>
R8C5 can only be <9>
Today's Sudoku Puzzles
All daily items change at midnight GMT – set your local time zone.
Note: BrainBashers has a Dark Mode setting.