Rule of 45 across several units
Two rows add to 90, three boxes to 135. Larger regions isolate cells that a single unit cannot.
What it is
The rule of 45 is not limited to one unit. Any combination of complete rows, columns or boxes has a known total: 90 for two, 135 for three. Applying it to a block of units often leaves exactly one cell unaccounted for, even when no single unit would.
How to spot it
Look for two or three adjacent units where the cages are largely contained. Add the contained cage sums, compare with the multiple of 45, and the difference belongs to the few crossing cells.
Worked example
Step through the example. First the position, then the cage the argument rests on, then the candidates, and finally what follows from it.
Step 1 of 4: The starting position
- Pattern cells
- 19 cells
- Digits
- 5
- Follows from it
- 3/8
Press a marked square to point it out on the board above.
Why it matters
Each unit contributes 45 independently, so a region of n units totals 45n. Cage sums partition the same cells differently; the discrepancy is exactly the total of cells crossing the region boundary.
Practise now
The practice puzzle is picked so that this technique is what gets the solve moving again.
Frequently asked questions
Which combinations are worth trying?
Adjacent units in the same band or stack — two rows of a box band, or two boxes side by side. Cages tend to stay within a band, so few cells cross.
Is there a limit?
In principle any region works, but beyond three units too many cages cross the boundary and the deduction stops paying off.
How does it relate to innies and outies?
It is the same idea on a larger region. Innies and outies over one unit; this is innies and outies over several.
Put it to use
Where you will meet it
Expert grids are the only place this pattern regularly decides the solve. Bring your notes.
Play ExpertStuck on a grid of your own?
Type the position into the solver and it walks the whole solution, naming the technique behind every step — including this one.
Open the solverFinished reading? Mark it done and the learning path remembers where you got to.