GridWits
Extreme tier Technique 20 of 20 Used by Smart Hint

Contradiction

Placing this digit here forces some run into an impossible position — so it can be ruled out.

How it works

  1. 1Nothing left on the ladder moves this position, so pick a candidate and find out what it costs.
  2. 2Suppose the top-right cell were 2: its down run is 7, so the cell below becomes 5, and the top row's other two cells are left needing 4 between them — only 1 then 3 will do.
  3. 3Follow those two down their own runs and both land on a 2, in the same bottom row — and a run never repeats a digit.
  4. 4The supposition breaks the board, so strike the 2. This is the last resort: it costs a full trial for every candidate you test.
3 5 7 6 1 2 2 3 1 2 3 9 1 2 2 3 4 5 6
  • Cells that establish the pattern
  • Where the conclusion lands
  • Digit ruled out