Killer Sudoku Cage Combinations — The Complete Cheat Sheet

Cubedoku Guides · Published 2026-06-11

Every Killer Sudoku puzzle is powered by one engine: knowing which digit combinations a cage sum allows. Most cages allow several; a precious few allow exactly one. Learn the forced cages by heart and you will open almost any Killer board without a single note — this page is the cheat sheet, plus how to actually use it. (New to the mode? Start with the Killer Sudoku rules guide.)

The forced cages — only one combination exists

These sixteen cage sums have exactly one set of digits. They are the strongest clues on any Killer board, so scan for them first:

  • 2 cells:3 = 1+2  ·  4 = 1+3  ·  16 = 7+9  ·  17 = 8+9
  • 3 cells:6 = 1+2+3  ·  7 = 1+2+4  ·  23 = 6+8+9  ·  24 = 7+8+9
  • 4 cells:10 = 1+2+3+4  ·  11 = 1+2+3+5  ·  29 = 5+7+8+9  ·  30 = 6+7+8+9
  • 5 cells:15 = 1+2+3+4+5  ·  16 = 1+2+3+4+6  ·  34 = 4+6+7+8+9  ·  35 = 5+6+7+8+9

Notice the symmetry: the two smallest and two largest possible sums for each cage size are always forced. You do not need to memorise sixteen facts — remember “extremes are forced” and you can reconstruct the list at the board.

The almost-forced cages — two combinations

One step weaker but still excellent: sums one away from the extremes allow exactly two sets. A 2-cell cage of 5 is 1+4 or 2+3; a 2-cell cage of 15 is 6+9 or 7+8. Either way you learn something immediately — a 5-cage contains no 5, 6, 7, 8 or 9, and a 15-cage contains nothing below 6. Often that alone kills candidates across the row.

What every 2-cell cage tells you for free

Even an unhelpful-looking sum carries two facts. First, the two digits cannot be equal, so a 2-cell cage summing to an even number never contains its half: a 12-cage has no 6, an 8-cage no 4. Second, each digit bounds the other — in a 9-cage, seeing a 2 anywhere in the cage's row or column instantly affects the 7. Cages are not just sums; they are live links between two cells.

Combine with the rule of 45

Combination knowledge multiplies with the other Killer fundamental: every row, column and box sums to 45. When an almost-complete box leaves one cell sticking into a neighbouring cage (an “innie”), the 45-arithmetic gives you that cell's exact value — and that value collapses its cage's combination list, which collapses the next cage, and so on. The full innie/outie walkthrough is in the rules guide; the speed comes from running both tools together.

A worked opening

Suppose a 3-cell cage of 24 sits in the top-left box, and a 2-cell 4-cage crosses it in the same box. The 24-cage is forced: 7+8+9. The 4-cage is forced: 1+3. That is five of the box's nine digits placed-or-paired before you have used any classic technique at all — and the remaining four cells now hold 2, 4, 5, 6 in some order, which your normal scanning habits will resolve quickly. Killer openings are usually this mechanical; the puzzle only gets subtle in the middle game.

How to practise

Drill the forced cages until recall is instant — at the board, hesitation costs more than ignorance. Then play a few Killer rounds focusing only on cage-first openings: play Killer free in your browser, or print one and solve it on paper with the daily printable Killer puzzle. Once cage arithmetic is automatic, you will find the mode reads less like maths homework and more like the purest form of Sudoku logic.

Keep reading

Or put it into practice — play Cubedoku free in your browser, no download or account needed.