GridWits
Easy tier Technique 3 of 31 Used by Smart Hint

Killer Combinations

A cage's total and size limit which distinct digit sets can live in it.

How it works

  1. 1Every cage holds distinct digits adding to its total, so only some digit sets are possible at all. A 2-cell cage totalling 17 can only be 8 and 9; a 3-cell cage totalling 7 can only be 1, 2 and 4.
  2. 2Strike every candidate that appears in no possible set. In that 3-cell 7-cage, nothing above 4 can appear anywhere in it.
  3. 3This is arithmetic only: it does not yet ask whether a surviving set can be assigned to the cage's particular cells. That stronger question is Cage Placement Support.
Next in the ladder Innies (Rule of 45) →

Every row, column and box totals 45. Subtract the cages inside it; one leftover cell is then known outright.