GridWits
Extreme tier Technique 16 of 20 Used by Smart Hint

Arrangement Check (Very Wide)

The same fit-the-cells check on a run offering seven or more combinations. Every one of them has to be dealt out against the run's cells, for each candidate you are testing.

How it works

  1. 1Three cells sum to 12, and that admits seven combinations: 1+2+9, 1+3+8, 1+4+7, 1+5+6, 2+3+7, 2+4+6 and 3+4+5.
  2. 2Each right-hand cell heads a 3-in-two down run, whose only combination is 1+2 — so between them they must supply exactly a 1 and a 2.
  3. 3Only 1+2+9 contains both, and every other combination leaves one of those cells with nothing it can take.
  4. 4So the left cell is 9. Seven combinations, each dealt out against the run's cells for every candidate tested, is why this band is priced Extreme on its own.
3 3 12 5 6 7 8 9 1 2 1 2 1 2 1 2
  • Cells that establish the pattern
  • Where the conclusion lands
  • Digit ruled out
Next in the ladder Surface Pair →

Two overlapping groups of runs differ by two cells — subtracting their clue totals fixes those cells' sum (or difference), ruling out any digit with no possible partner.