Contradiction
Placing this digit here forces some run into an impossible position — so it can be ruled out.
How it works
- 1Nothing left on the ladder moves this position, so pick a candidate and find out what it costs.
- 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.
- 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.
- 4The supposition breaks the board, so strike the 2. This is the last resort: it costs a full trial for every candidate you test.
- Cells that establish the pattern
- Where the conclusion lands
- Digit ruled out