GridWits
Medium tier Technique 5 of 20 Used by Smart Hint

Run Bounds

Test one candidate against the smallest and largest distinct totals the other cells can still make. If the needed remainder lies outside those bounds, remove it.

How it works

  1. 1The three cells must total 17, and the first cell is currently 2 or 3.
  2. 2If the first cell were 3, the other two would have to total 14. But their distinct candidates can total no less than 8 + 7 = 15.
  3. 3So 3 is outside the run's reachable bounds and can be struck. A 2 remains possible because 8 + 7 supplies the required 15.
  4. 4This checks only the smallest and largest reachable totals; Arrangement Check later handles gaps inside that interval.
17 2 3 8 9 7 9
  • Cells that establish the pattern
  • Where the conclusion lands
  • Digit ruled out
Next in the ladder Partner Check →

Only two cells of this run are empty, so they split the remaining sum between them — a digit whose partner (remaining sum minus it) can't go in the other cell is impossible.