GridWits
Hard tier Technique 13 of 31 Used by Smart Hint

Cage Placement Support

A digit survives only if a complete cage assignment can place it in that particular cell.

How it works

  1. 1Take a 2-cell cage totalling 10: its arithmetic sets are 1+9, 2+8, 3+7 and 4+6.
  2. 2Suppose the row already holds 1, 2 and 3 elsewhere, so neither cage cell may take those digits.
  3. 3The first three sets each need a digit that has no legal cell. Only 4+6 admits a one-to-one assignment.
  4. 4Strike 7, 8 and 9 from both cells. Those digits passed the Easy sum table, but fail the harder cell-placement proof.
Next in the ladder Innies/Outies (2+ cells) →

When several cells are left over after subtracting a house's whole cages, their total constrains all of them at once.