GridWits
Extreme tier Technique 17 of 20 Used by Smart Hint

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.

How it works

  1. 1Same subtraction as Surface Sum: the down clues total 4 + 7 = 11 over the tinted block, the across clues total 4 + 13 = 17 over that block plus the row's last two cells.
  2. 2So those two cells add to 17 − 11 = 6, even though neither is pinned down yet.
  3. 3The right-hand one heads a 3-in-two down run, so it is a 1 or a 2 — which leaves its partner a 5 or a 4, never a 6.
  4. 4Strike the 6. A pair sum is weaker than a placement, but it prices two cells against each other from clues alone.
4 7 3 4 1 3 1 3 1 2 13 1 3 4 6 4 5 6 1 2
  • Cells that establish the pattern
  • Where the conclusion lands
  • Digit ruled out
Next in the ladder Surface Triple →

Two overlapping groups of runs differ by three cells — subtracting their clue totals ties those three digits together, ruling out any that can't be completed.