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
- 1The innie rule is at its most useful with one leftover cell, but it still says something with two, three or four.
- 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.
- 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.
- 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.
- 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.