Outies (Rule of 45)
The cages touching a house cover it plus a spill. When the spill is one cell, their excess over 45 is that cell.
How it works
- 1Every cell of a house belongs to some cage, so the cages that touch a house always cover all nine of its cells — plus whatever those cages spill outside it.
- 2Take a box touched by three cages: 15 across three cells and 17 across four, both wholly inside, and 20 across three that keeps two cells in the box and drops one into the box below.
- 3The innie form stalls here. The whole cages leave TWO cells over, not one, so 45 − 32 = 13 names a pair and no cell.
- 4The spilling cage is no help either: 20 across three cells allows anything from 3 to 9, so the cell you are after still carries seven marks and is no kind of single.
- 5So add the touching cages instead: 15 + 17 + 20 = 52. They cover 45 worth of box plus the single cell lying outside it, so that 'outie' is 52 − 45 = 7.
- 6This reaches a cell the innie rule cannot: the answer lands OUTSIDE the house you measured.