Innies and outies
Cells reaching into a unit from outside are innies; cells reaching out are outies. The rule of 45 gives their total.
What it is
Cages rarely align with unit boundaries. A cage may lie mostly in one box with a single cell poking into the next. Add the sums of all cages that overlap a unit and compare with 45: the difference tells you exactly what the protruding cells add to — even before you know any of them individually.
How to spot it
Look for units where one or two cells belong to cages that mostly sit elsewhere. Single innies and single outies are the strongest: their digit follows immediately.
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
- 1/1, 1/2, 1/3, 2/1, 2/2, 2/3, 3/1, 3/2, 3/3, 4/3
- Digits
- 2
- Follows from it
- 4/3
Press a marked square to point it out on the board above.
Why it matters
The unit adds to 45. Cages overlapping it contribute their full sums, including the parts outside. Subtracting 45 leaves precisely the total of the cells lying outside — the outies. The same reasoning in reverse gives the innies.
Practise now
The practice puzzle is picked so that this technique is what gets the solve moving again.
Frequently asked questions
What is the difference between an innie and an outie?
An innie is a cell inside the unit whose cage lies mostly outside. An outie is a cell outside the unit whose cage lies mostly inside.
When is the deduction strongest?
With exactly one innie or outie. Then the difference from 45 is that cell's digit, with no further work.
Can I combine several units?
Yes, and that is where it gets powerful: two boxes total 90, three rows 135. Larger regions often isolate a single protruding cell.
Put it to use
Where you will meet it
Hard grids are built around moves like this one. That is where it earns its keep.
Play HardStuck 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.
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