Jan 01 - Super Hard
Puzzle Copyright © Kevin Stone
Share link – www.brainbashers.com
Reasoning
R7C5 can only be <2>
R8C9 is the only square in row 8 that can be <3>
R9C9 can only be <1>
R9C8 can only be <8>
R9C1 can only be <7>
R9C2 can only be <3>
R5C3 is the only square in column 3 that can be <7>
R3C3 is the only square in column 3 that can be <5>
R3C7 is the only square in column 7 that can be <7>
R3C8 is the only square in column 8 that can be <3>
R3C5 can only be <9>
R3C2 can only be <1>
R2C7 is the only square in row 2 that can be <1>
R2C3 is the only square in row 2 that can be <9>
R7C3 can only be <1>
R8C3 can only be <8>
R8C1 can only be <6>
R8C7 can only be <9>
R7C2 can only be <9>
R1C8 is the only square in row 1 that can be <9>
R2C9 is the only square in row 2 that can be <6>
R1C9 can only be <4>
R1C1 can only be <8>
R1C2 can only be <6>
R2C1 can only be <4>
R5C4 is the only square in row 5 that can be <9>
Squares R4C2 and R4C4 in row 4 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 row.
R4C5 - removing <5> from <357> leaving <37>
R4C6 - removing <2> from <2347> leaving <347>
Squares R5C6<14>, R5C7<46> and R5C8<146> in row 5 form a comprehensive naked triplet. These 3 squares can only contain the 3 possibilities <146>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the row.
R5C5 - removing <6> from <568> leaving <58>
R6C5 is the only square in column 5 that can be <6>
Squares R7C7, R7C8, R5C7 and R5C8 form a Type-1 Unique Rectangle on <46>.
R5C8 - removing <46> from <146> leaving <1>
R5C6 can only be <4>
R6C8 can only be <7>
R4C8 can only be <4>
R7C8 can only be <6>
R5C7 can only be <6>
R7C7 can only be <4>
The puzzle can be reduced to a Bivalue Universal Grave (BUG) pattern, by making this reduction:
R6C4=<18>
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
R6C4 - removing <18> from <128> leaving <2>
R6C2 can only be <8>
R6C6 can only be <1>
R2C4 can only be <8>
R4C4 can only be <5>
R8C6 can only be <7>
R8C5 can only be <5>
R4C6 can only be <3>
R2C5 can only be <3>
R2C6 can only be <2>
R4C5 can only be <7>
R4C2 can only be <2>
R8C4 can only be <1>
R5C5 can only be <8>
R5C2 can only be <5>
Today's Sudoku Puzzles
All daily items change at midnight GMT – set your local time zone.
Note: BrainBashers has a Dark Mode option – I recommend not using your browser's dark mode or extensions for BrainBashers