sudokUI › Sudoku techniques › Digit Forcing Chain
Digit Forcing Chain in sudoku
One candidate is followed both ways, once assumed true and once assumed false, each time placing the naked and hidden singles that follow, and the two results are compared.
Why it works
The candidate is either true or false, so whatever both runs agree on is certain: a digit both place in the same cell is placed, a candidate both remove is eliminated. If the false run ends in a contradiction, the candidate itself is placed.
How to spot it
Start from a candidate in a bivalue cell or a conjugate pair, because there the false run also forces a placement straight away.
Worked example
Digit forcing: whether r1c1 is 8 or not, the forced singles agree on the same conclusions.
The solver uses this on the hardest puzzles. It has no pattern to spot, so it is not offered in practice.
In a puzzle's rating
Each time the solver needs Digit Forcing Chain, the puzzle's difficulty rating grows by 500. Its class is Extreme. It is needed in 1 in 180 puzzles that sudokUI generates. How the rating works.
More last resort
Exocet · Double Exocet · Pattern Overlay · Forcing Chain · Nishio Forcing Chain · Cell Forcing Chain · Unit Forcing Chain · Forcing Net · Brute Force