Cage combinations
A cage sum plus its size limits which digits can appear. A two-cell cage summing to 3 can only be 1 and 2 — no other pair works.
What it is
Every cage carries a sum and a number of cells, and because digits inside a cage never repeat, only certain sets of digits can produce that sum. A two-cell cage adding to 3 must be 1+2. A three-cell cage adding to 7 must be 1+2+4. These forced sets are the bedrock of Killer Sudoku: before any elimination, they tell you which digits are even in play.
How to spot it
Look for the extremes first. Small sums in small cages and large sums in small cages are the most restrictive: 3 in two cells, 4 in two cells, 6 in three cells, or at the other end 17 in two cells and 24 in three cells. These have exactly one possible digit set.
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
- 3/3, 4/3
- Digits
- 1, 2
- Follows from it
- —
Press a marked square to point it out on the board above.
Why it matters
Inside a cage no digit may repeat, so the digits form a set of distinct values between 1 and 9. For a given cage size only a limited number of such sets reach the required total. If exactly one set does, every cell in the cage is restricted to those digits — often enough to solve neighbouring cells straight away.
Practise now
The practice puzzle is picked so that this technique is what gets the solve moving again.
Frequently asked questions
How do I work out a cage combination quickly?
Start from the smallest digits. For a two-cell cage summing to 4 the smallest pair is 1+3; 2+2 is not allowed because digits cannot repeat inside a cage. So 1 and 3 is the only option.
Which cages are the most useful to look at first?
Cages whose sum is close to the minimum or maximum for their size. A two-cell cage of 3 or 17, or a three-cell cage of 6 or 24, each have exactly one digit set.
Do cage combinations alone solve a puzzle?
Rarely on their own, but they narrow the candidates enough that ordinary Sudoku logic takes over. In easy Killer puzzles that combination is often the whole solve.
Put it to use
Where you will meet it
Medium grids are where this move starts to matter: the obvious cells run out and the pattern takes over.
Play MediumStuck 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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