Innies (Rule of 45)
Every row, column and box totals 45. Subtract the cages inside it; one leftover cell is then known outright.
How it works
- 1A house holds 1 through 9 exactly once, so its digits always add to 45. That is the whole basis of Killer arithmetic.
- 2Take a box covered by three cages sitting ENTIRELY inside it: 15 across three cells, 9 across two, and 14 across the remaining three. They total 38 and cover eight of the nine cells.
- 3None of them pins a digit on its own — 15 across three cells has eight possible sets, 14 across three has eight more, 9 across two has four — and every digit still has several homes in the box, so there is no single to find here.
- 4The ninth cell is the 'innie'. It belongs to a 4-cell cage totalling 20 that runs on into the next box, and 20 across four cells allows every digit from 1 to 9, so its own arithmetic says nothing whatever about it.
- 5Only the house does: the other eight cells take 38 of its 45, so the innie is 45 − 38 = 7.
- 6The cages must be wholly inside the house for this to work. A cage that pokes out contributes part of its total to a cell you are not counting.