GridWits
Hard tier Technique 14 of 31 Used by Smart Hint

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.

How it works

  1. 1The innie rule is at its most useful with one leftover cell, but it still says something with two, three or four.
  2. 2Say a row carries a 2-cell cage totalling 13 and a 4-cell cage totalling 25 — 38 across six cells — and each of its other three cells belongs to a 3-cell cage of 15 dropping into the row below.
  3. 3Those spilling cages allow every digit from 1 to 9, so cage arithmetic says nothing about the three, and the single-cell innie rule wants one leftover cell, not three.
  4. 4But the three must total 45 − 38 = 7, and being in one row their digits differ — the only three distinct digits totalling 7 are 1, 2 and 4.
  5. 5Strike 3, 5, 6, 7, 8 and 9 from all three at a stroke, then keep checking placement the way Killer Combinations does. If one of the three sits in a column that already holds a 2, that cell is down to 1 and 4.
Next in the ladder Multi-House Rule of 45 →

Two rows total 90, three total 135 — bands of houses have whole cages to subtract where a single house has only fragments.