Sudoku-YFoundations
The rule of 45: count the cells before subtracting
Nearly covered a whole row with cages? Step back from individual digits and try adding the cage totals.
Where 45 comes from
A row, column or box in 9×9 Sudoku contains 1–9 once each, giving a total of 45. That total is known before the order is known. A cage instead uses its printed total; a cage is not automatically a complete Sudoku unit.
Killer Sudoku Online — Solving strategies · SudokuWiki — Innies and Outies
Our example: one cell left over
In this partial teaching scenario, three cages lie entirely inside row A. They cover A1–A8 exactly once and have totals 10, 13 and 15. Together they account for 38, so the remaining cell is A9=45−38=7. We do not need to settle the order inside the 13 cage first.
The exact coverage matters. Every included cell must be counted once, with no gaps or overlaps. The arithmetic is simple only after that boundary check.
A crossing cage changes the equation
If the 15 cage also includes B8, its whole total no longer describes cells inside row A. Subtracting all 38 would subtract B8 as well. Write the cell names beside each cage total and mark any outside cells. If B8 is known, remove its value from the cage total first; otherwise use an innie/outie equation.
The total changes with the board
The sum from 1 to n is n(n+1)/2. Sudoku-Y therefore uses 10 for 4×4, 21 for 6×6 and 136 for 16×16. These boards use the numeric values 1 through their size. Do not carry the number 45 into a smaller game just because the technique has that name.
Try before looking
Try before revealing
Five cells of a 6×6 Killer row are exactly covered by cages totaling 17. What is the last cell?
Show explanation
It is 4: the row totals 21, and 21−17=4. The five cells must belong entirely to that row and be counted once.
References and further reading
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