Cage Splitting — Killer Sudoku Technique
A cage that straddles two units splits into two sub-regions whose sums are individually constrained by the cages around them.
Killer Sudoku sudoku technique
What it is
When a cage spans two or more units (rows, columns, or boxes), you can split it into the part inside each unit. Each part has an unknown sub-sum, but the 45 rule applied to the surrounding cages often pins that sub-sum to a small range. Once a sub-sum is bounded, the combinations cheat sheet narrows the actual digit set inside that sub-region. Combine that with the rest of the cage and you've split one big cage-level deduction into two tighter ones. Cage splitting is most powerful on large 4–6-cell cages crossing multiple units, because each split exposes a smaller sub-cage that the cheat sheet pins down decisively.
When to use it
On crossing cages of 3+ cells, after the 45 rule has bounded a sub-region's sum. Most valuable in expert and master Killer puzzles where pure 45-rule deductions have stalled.
Worked example
A 5-cell cage summing to 25 spans box 1 (3 cells: R1C1, R1C2, R2C1) and box 2 (2 cells: R1C4, R1C5). Box 1's other cages sum to 18, so by the 45 rule the box-1 portion of this cage must sum to 45 − 18 = 27 − (cells of OTHER crossing cages). After narrowing, the box-1 portion sums to some value S1; the box-2 portion then sums to 25 − S1. Apply the combinations cheat sheet to each half — for a 3-cell sub-region summing to a tightly-bounded value, the digit set often collapses to one or two combinations.
Try it
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