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Innies and outies: missing cells and extra cells
Think of the names as a missing piece inside a boundary and an extra piece outside it.
Pick a boundary first
A 9×9 row, column or box totals 45. Entirely internal cages may leave uncovered inside cells, or innies. A collection of cages that covers the unit may extend into outside cells, or outies. Draw that boundary mentally before doing the arithmetic.
Killer Sudoku Online — Solving strategies · SudokuWiki — Innies and Outies
Our inside example
Suppose internal cages cover eight cells of row D exactly once and total 37. D9 is the only uncovered cell, so D9=45−37=8. If two cells were uncovered, the subtraction would establish their combined total, not each individual value.
Our outside example
In a separate scenario, disjoint cages cover all nine cells of row D and only one additional cell, E9. The cage totals add to 47. Write “row D + E9 = 47”; then E9=47−45=2. Writing the covered area as an equation helps keep the subtraction the right way around.
If F9 were also outside, the equation would instead give E9+F9=2. Check whether positive digits and no-repeat constraints even allow that situation. Dividing by two and entering two 1s would not be justified.
A derived sum is not automatically a cage
Two outside cells may repeat a digit if they share neither a Sudoku unit nor an actual cage. A useful derived total does not create an extra no-repeat rule. Before borrowing a combination table for real cages, check the relationship between the derived cells.
Sudoku-Y’s Killer hints do not currently search for advanced innie/outie deductions. This lesson helps you inspect them yourself.
Try before looking
Try before revealing
Cages cover one whole row plus two outside cells and total 52. What follows?
Show explanation
The outside cells total 7. Their order and whether repetition is forbidden still depend on their actual rows, columns, boxes and cages.
References and further reading
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